text: On 24 January, the Taiwanese government announced a temporary ban on the export of face masks for a month to secure a supply of masks for its own citizens. On 2 February 2020, Taiwan's Central Epidemic Command Center postponed the opening of primary and secondary schools until 25 February. Taiwan has also announced a ban of cruise ships from entering all Taiwanese ports. In January, Italy has banned flights from mainland China, Hong Kong, Macau, and Taiwan. On 10 February, the Philippines announced it will ban the entry of Taiwanese citizens due to the One-China Policy. Later on 14 February, Presidential Spokesperson of Philippines, Salvador Panelo, announced the lifting of the temporary ban on Taiwan. In early February 2020 Taiwan's Central Epidemic Command Center requested the mobilisation of the Taiwanese Armed Forces to contain the spread of the virus and to build up the defences against it. Soldiers were dispatched to the factory floors of major mask manufacturers to help staff the 62 additional mask production lines being set up at the time.


title: Economic impact of the COVID-19 pandemic

text: In the aviation industry, Taiwanese carrier China Airlines's direct flights to Rome have been rejected and cancelled since Italy has announced the ban on Taiwanese flights. On the other hand, the second-largest Taiwanese carrier, Eva Air, has also postponed the launch of Milan and Phuket flights. Both Taiwanese airlines have cut numerous cross-strait destinations, leaving just three Chinese cities still served.


text: In India, economists expect the near-term impact of the outbreak to be limited to the supply chains of major conglomerates, especially pharmaceuticals, fertilisers, automobiles, textiles and electronics. A severe impact on global trade logistics is also expected due to disruption of logistics in mainland China, but due to the combined risk with regional geopolitical tensions, wider trade wars and Brexit. The stock market took a bearish mode in response to COVID-19. The BSE SENSEX fell 2919 and NIFTY 50 fell 950 points in a single day on 12 March 2020.


text: On 19 March 2020, the Indian government has banned the export of ventilators, surgical/disposable masks and textile raw materials out of the country.


text: Oil has plummeted to 18-year low of $22 per barrel in March, and Foreign Portfolio Investors (FPIs) have withdrawn huge amounts from India, about US$571.4 million. While lower oil prices will shrink the current account deficit, reverse capital flows will expand it. Rupee is continuously depreciating. MSMEs will undergo a severe cash crunch.


text: The economy of Pakistan faced a devastating impact from the coronavirus outbreak because it was in recessionary conditions in the quarter prior to the pandemic. Weak social protections and low investment in healthcare meant that most citizens were vulnerable to pandemic conditions at the time of the outbreak. Forecasts of the economic loss from the three-month lockdown, which was subsequently eased in late May 2020, indicated that Pakistan would face its first annual economic recession since 1952. Given the strained government resources, civil society and charity organizations became much more active in providing relief to the public during the national lockdown.


text: In February 2020, research houses expected the economic impact in Sri Lanka to be limited to a short-term impact on the tourism and transport sectors.


text: Among Association of Southeast Asian Nations countries, the city-state of Singapore was forecast to be one of the worst-hit countries by Maybank. The tourism sector was considered to be an "immediate concern" along with the effects on production lines due to disruption to factories and logistics in mainland China. Singapore has witnessed panic buying of essential groceries, and of masks, thermometers and sanitation products despite being advised against doing so by the Government. Prime Minister Lee Hsien Loong said that a recession in the country is a possibility and that the country's economy "would definitely take a hit". On 17 February, the Ministry of Trade and Industry (MTI) downgraded Singapore's forecast GDP growth to between −0.5% and 1.5%. This is largely due to the fall in tourism and social distancing restrictions. On 26 March, MTI said it believed that the economy would contract by between 1% and 4% in 2020. This was after the economy shrank some 2.2% in the first quarter of 2020 from the same quarter in 2019. On 26 May, the Singapore economy contracted 0.7%YoY, which was better than the expected contraction of 2.2%. However, MTI said that it was revising down its expectation for the Singapore economy in 2020 to shrink by 4% to 7%. Economists were behind the curve in downgrading their numbers. Euben Paracuelles, at Nomura argued that while some ASEAN economies had success in containing the virus, the presence of global uncertainties meant that any regional recovery would be restrained. For example, while Thailand had managed to contain the virus, it was not open to tourism, which forms a substantial part of its economy.


text: Prime Minister Hun Sen of Cambodia made a special visit to China with an aim to showcase Cambodia's support to China in fighting the outbreak of the epidemic.


text: Maybank economists rated Thailand as being most at risk, with the threat of the viral outbreak's impact on tourism causing the Thai baht to fall to a seven-month low.


text: In Indonesia, over 10,000 Chinese tourists cancelled trips and flights to major destinations such as Bali, Jakarta, Bandung, etc., over coronavirus fears. Many existing Chinese visitors are queuing up with the Indonesian authority appealing for extended stay. Panic buying has also hit the capital city, Jakarta. As the first reported cases of COVID-19 was announced by the government at 3 March.


text: In Malaysia, economists predicted that the outbreak would affect the country's GDP, trade and investment flows, commodity prices and tourist arrivals. Initially, the cycling race event Le Tour de Langkawi was rumoured to be cancelled, but the organiser stated that it would continue to be held as usual. Despite this, two cycling teams, the Hengxiang Cycling Team and the Giant Cycling Team, both from China, were pulled from participating in this race due to fear of the coronavirus pandemic. As the outbreak situation has worsened, some of the upcoming concerts held in the country, such as Kenny G, Jay Chou, Joey Yung, The Wynners, Super Junior, Rockaway Festival and Miriam Yeung, were postponed to a future date, and the upcoming Seventeen concert was cancelled.


text: The Philippines reported that its GDP contracted by 9.5% in 2020, its worst contraction since World War II. The last full-year contraction in the country was in 1998 amidst the Asian financial crisis where its GDP grew by −0.5%. The 2020 contraction was also worse than the 7% contraction in 1984.


text: Vietnam, who had clamped down early to prevent the spread of the coronavirus, was expected to be the only country in the South East Asia region that was expected to grow in 2020.


text: On 26 March, Rouhani requested to withdraw 1 billion dollars from National Development Fund and Khamenei allowed the withdrawal within eleven days. On 28 March, Rouhani announced that 20% of the country's annual budget would be allocated to fight the virus. The following day, he defended against criticisms of the government's response to the outbreak, saying that he needed to weigh protecting the country's economy that was already affected by US sanctions while fighting the worst outbreak of the region.


text: At its peak, Israel was one of the world's worst hit countries from the COVID-19 pandemic. By 1 April 2020, the national unemployment rate had reached 24.4 percent. In the month of March alone, more than 844,000 individuals applied for unemployment benefits—90% of whom had been placed on unpaid leave due to the pandemic. Following the world's fastest and most successful vaccination campaigns by far using the Pfizer-BioNTech jab, Israel currently issues 'green passports' for individuals who have received their 2nd vaccine dose; which allow indefinite access to many places and amenities formerly only accessible to those with a negative COVID-19 test result. The subsequent low-infection rates have eased restrictions and the economic tension in the country.


text: As of 29 March 2021; 5,227,689 Israelis have received at least 1 dose of the vaccine, out of which 4,739,694 have had 2 doses.


text: On 30 March 2020, Prime Minister Netanyahu announced an economic rescue package totaling 80 billion shekels ($22 billion), saying that was 6% of the country's GDP. The money will be allocated to health care (10 billion₪); welfare and unemployment (30 billion₪) aid for small and large businesses (32 billion₪), and to financial stimulus (8 billion₪).


text: Israel agreed to pay Russia to send Russian-made Sputnik V vaccine doses to Syria as part of a Russia-mediated prisoner swap agreement.


text: In 2020, Israel's economy shrank by 2.4%, following 3.4% and 3.5% growth in 2019 and 2018 respectively. This is considerably below the Euro-bloc where the economy shrank by 5%.


text: On 27 February, Saudi Arabia halted travel to Mecca and Medina over coronavirus. This has prevented foreigners from reaching the holy city of Mecca and the Kaaba. Travel was also suspended to Muhammad's mosque in Medina. Images of the emptied "ṣaḥn" of the Great Mosque of Mecca, where pilgrims are ordinarily performing the "tawaf" around the Kaaba, went viral on social media.


text: The COVID-19 pandemic reportedly pressured the property sector, which has already been dealing with the imbalance between supply and demand for years. Dubai's property firms, Emaar Properties, and DAMAC Properties reported losses following the surge in COVID-19. Emaar reported a 58% loss in net profit while DAMAC Properties reported a net loss of 1.04 billion dirhams in the year 2020.


text: In March 2021, the restrictions on global supply-chain caused a great impact on Dubai's business activities, which were struggling to recover from the impact of the Covid-19 pandemic. The IHS Markit compiled Dubai's Purchasing Managers’ Index that rose to 51 from 50.9 in February 2021, saving from landing in the contraction zone by only one point. The global supply difficulties also led to "constraint profit margins", as the need of demand recovery forced firms to lower output charges.


text: Jordan's real GDP fell by 1.6% in 2020, with a dramatic reduction in tourism, one of its most crucial economic sectors. The sector's GDP fell by 3%.


text: SMEs appeared less affected by the pandemic than bigger enterprises. 50% of banks questioned reported an increase in loan supply to SMEs, while 25% reported a reduction. For corporates, the increase in loan supply was 25% and 45% reported a reduction. The country's unemployment rate hit 25% in 2021, the highest in more than 25 years.


text: Macroeconomic stability, however, has been maintained, and the International Monetary Fund expects modest growth rates for 2022 (2.7%) and 2023 (2.7%) in predictions provided in the October 2021 World Economic Outlook. In the first half of 2021, real GDP increased by 3.2%.


text: In Spain, a large number of exhibitors (including Chinese firms Huawei and Vivo) announced plans to pull out of or reduce their presence at Mobile World Congress, a wireless industry trade show in Barcelona, due to concerns over coronavirus. On 12 February 2020, GSMA CEO John Hoffman announced that the event had been cancelled, as the concerns had made it "impossible" to host.


text: Owing to an increase in the demand for masks, on 1 February most masks were sold out in Portuguese pharmacies. On 4 February, President Marcelo Rebelo de Sousa admitted that the epidemic of the new coronavirus in China "affects the economic activity of a very powerful economy and thus affects the world's economic activity or could affect". He also admitted the possibility of economic upheavals due to the break in production." On 28 February, the Swiss government has banned all public and private gatherings of more than 1,000 people until 15 March, including forcing through a cancellation of the Geneva International Motor Show.


text: European Commissioner for Internal Market and Services Thierry Breton has asked streaming video services operating in the EU to reduce the amount of bandwidth used by their services to preserve capacity and infrastructure. Netflix and YouTube havecomplied with this request.


text: Before the COVID-19 pandemic, about 86% of EU enterprises were making investments. In 2021 this remained mostly steady compared to 2020 (81%). EU businesses were optimistic for investment throughout 2022, with 20% more anticipating investment to rise than fall.


text: According to the a survey on investment conducted by the European Investment Bank, European firms lost one-quarter of their gross income on average in the second quarter of 2020. The loss was substantially greater than the drop experienced by enterprises during the global financial crisis in 2008 and the European sovereign debt crisis in 2010.


text: The European Investment Bank estimates that corporate investment in the EU could fall by between 31% and 52%, even in more favourable scenarios due to the pandemic. They also estimate that even after strong policy intervention, 51–58% of EU firms face liquidity shortfalls after 3 months of lockdown. 34% of enterprises also projected their capacity to fund internal investments to decline in the coming 12 months. The European Investment Bank Group created a €25 billion Pan-European Guarantee fund to help small businesses recover from the COVID-19 crisis. As a result of this guarantee fund, the EIB Group, in partnership with local lenders and national promotional institutions, is able to increase its support to small and medium-sized companies.


text: Small businesses have been hit hard by the COVID-19 pandemic and its lockdowns. Many of them also lacked the technological tools to survive in an unprecedented environment. To make things worse, in the European regions most affected by the coronavirus pandemic small businesses are usually less digitalised.


text: Less than 20% of European small and medium-sized enterprises (SMEs) are highly digitalised, whereas almost 50% of large corporations are digitalised, having an economic impact. Small businesses are the engine of the European economy and they play a vital role in our economic recovery and growth. These businesses need financial support for their digitalisation. In response to COVID-19, almost 60% of EU businesses have received financial help – subsidies or other non-repayable aid. Enterprises that incurred sales losses were more likely to get policy help (about 73% received financial assistance, compared to 47% of firms that did not see any sales declines).


text: Due to the COVID-19 pandemic, 49% of enterprises in the European Union saw a drop in sales in 2021, compared to 21% who saw a boost. Digital businesses withstood the pandemic better than enterprises that were less productive before the crisis. Sales were down more for Small businesses, by at least 25%, than for medium or large businesses. In response to fewer sales, 23% reduced their investment intentions, while just 3% intended to increase their investment. The share of companies that invested dropped from 86% in 2019 to 79% in 2021.


text: Furlough and short-term employment programmes in the European Union kept people employed, while bankruptcy filing rules for businesses were reduced, allowing workers to keep their jobs. A significant portion of businesses benefited from the policy support for the COVID-19 shock across all EU regions. The most prevalent forms of assistance across all areas were subsidies or other non-repayable support measures, including support for furlough programs. Inequality existed across EU regions. Compared to enterprises in less developed regions (40%) or non-cohesion regions (37%) firms in transition regions were less likely to get subsidies (28%).


text: Since the beginning of 2020, EU enterprises that embraced advanced digital technology and invested in becoming more digital during the pandemic have increased the number of employees they employ. After the COVID-19 outbreak, the number of non-digital enterprises that downsized was also greater than the share of non-digital firms that had positive job growth. Non-digital companies had a negative net employment balance.


text: Eastern Europe (together with Central Asia) saw a dramatic drop in economic activity as a result of COVID-19. GDP in the region fell by 4% on average in 2020, with businesses in contact-intensive service industries being particularly adversely impacted. However, the level of governmental support was vast, with fiscal measures totaling about 6% of GDP. The majority of businesses suffered losses in 2020 and/or 2021, with 13% still predicting that they won't be able to recover from the pandemic-era loss of business until 2022.


text: When compared to the final quarter of 2019, investment levels in several nations decreased or were flat in the second quarter of 2022. Denmark, Italy, Ireland, and Sweden are exceptions, with investment levels increasing by more than 10%. Other nations had drops in investment of up to 13%, such as Slovakia and Bulgaria.


text: The Armenian Government tried to confront the influence of the pandemic by implementing mitigation measures plus a lockdown. This adversely impacted businesses in Armenia, which either shut down or did not work with the same capacity as before. One of the consequences of this was supply shock. The supply shock caused a sharp decrease in sales. Companies adopted policies like reduction of working hours and wages, and workforce reductions. This led to the reduction in per capita income.


text: The IMF estimated that the contribution of the final consumption expenditure had diminished in 2020 by 2.1% (from 3.3% up to 1.2%). The production decreases led to a drop in corporate tax revenue. Moreover, public expenditures sharply increased to help companies and households. However, this caused a budget deficit and increasing external debt.


text: The financial difficulties caused by the pandemic also affected loan repayments and led to a sharp decrease in savings. The Armenian National Statistical Service mentioned that in the first 3–4 months of 2020, wages were increased by 6.8%, which helped citizens during the pandemic. The United Nations assessed that the loan/GDP ratio, which stood at 52.1% as of September 2020, would lead to an overall decrease in loan portfolio performance, as many loans would go unpaid. The limitations on international travel during the pandemic affected the international trade of goods and services. Predictions of the IMF in 2020 assumed that there would be a decline (60% in total) of the influx of the personal remittances and foreign direct investments.


text: Around AMD 26 billion (USD 55 million), according to official cost estimates, has been set aside for the implementation of the thirteen social assistance programs. The majority of spending (USD 25 million) has gone toward providing salary support to workers in the impacted industry, followed by family benefits (USD 15 million) and electricity bill subsidies (USD 10 million). Each participant received a one-time benefit of between USD 53 and USD 270.


text: Because of the pandemic, the economy of Armenia wasn't able to generate enough savings to finance investments. Concurrently, the Armenian economy was unable to generate enough exports to finance the imports, which caused an expanding trade deficit of around USD 2.9 billion in 2019. The Covid-19 Pandemic impacted the Armenian economy, and as a result the GDP dropped on average by 5.3% from January to August 2020.


text: On 8 April, the Bank of France officially declared that the French economy was in recession, shrinking by 6 percent in the first quarter of 2020.


text: According to the Deutsche Bank the outbreak of the novel coronavirus / COVID-19 May contribute to a recession in Germany.


text: By mid-March, nearly 3% of Ireland's population—140,000 people (including 70,000 restaurant staff, 50,000 pub and bar staff)—had lost their jobs due to restrictions brought in to delay the virus's spread. The numbers of people in normally busy Dublin areas such as Grafton Street dropped by percentages in the sixties, seventies and eighties.


text: On 16 March, Minister for Employment Affairs and Social Protection Regina Doherty announced the COVID-19 Pandemic Unemployment Payment. Initially available for six weeks, it was extended for another nine weeks on 5 June. On 24 March, the Temporary COVID-19 Wage Subsidy Scheme was announced for a twelve-week run beginning on 26 March.


text: On 15 May, Minister for Business, Enterprise and Innovation Heather Humphreys announced details of a new €250m "Restart Grant" which would give direct grant aid of between €2,000 and €10,000 to small businesses to help them with the costs associated with reopening and re-employing workers following the COVID-19 closures.


text: On 22 May, the Government of Ireland had signed off on €6.8 billion in extra funding for the Department of Employment Affairs and Social Protection, as it was due to reach this year's spending limit early the following month.


text: On 23 July, the Government of Ireland launched a €7.4 billion July Jobs Stimulus package of 50 measures to boost economic recovery and get people back to work. The measures include the extension of the COVID-19 Pandemic Unemployment Payment to April 2021, and the replacement of the Temporary COVID-19 Wage Subsidy Scheme to the Employment Wage Subsidy Scheme from September 2020 and will run until April 2021.


text: On 7 September, it was announced that Ireland was now officially in recession after the economy shrank by 6.1% between April and June as the impact of COVID-19 brought the largest quarterly drop on record, following new figures published by the Central Statistics Office.


text: On 21 February, at least ten towns in the Lombardy and Veneto regions of Italy, with a total population of 50,000, were locked down in quarantine procedure following an outbreak in the town of Codogno in Lombardy. Police mandated a curfew closing all public buildings and controlling access through police checkpoints to the so-called 'red zone' which is enforced under penalty by fines against trespassers who are not health or supply workers. The government of Italian Prime Minister Giuseppe Conte vowed that sending in "the armed forces" to enforce the lockdown was within possibility. Schools and universities have been closed throughout Northern Italy along with museums, and various festivities, concerts, sporting events and church masses have been cancelled as of 23 February. On 4 March, these closures were extended to all schools and universities nationwide.


text: Sustained panic buying of groceries has reportedly cleared out supermarkets, and several major events were cancelled, such as the annual Carnival of Venice, along with the cancellation of Serie A football matches on 23 February by the Sports Ministry. Concerns about the Milan Fashion Week has led to several fashion houses declaring that they will only hold broadcast, closed-door shows with no spectators. As of 26 February 2020, there have been 456 coronavirus cases in Italy, 190 of which have been also confirmed by the Istituto Superiore di Sanità.


text: By 12 March 2020, the number of cases in Italy had risen to 15,113, including 1,016 fatalities. On 9 March 2020, Italy declared a nationwide quarantine. Since 10 March 2020, all residents need a special form to be allowed to leave their homes. On 11 March 2020, all shops and businesses were closed except food shops and pharmacies. After the "Sostegni Decree" of 23 March 2021, the Italian government has ended the ban on collective dismissals since 1 July, except for the textile, fashion and footwear economic sectors for which it has been extended until 31 October.


text: Due to an increase in the demand for masks, on 1 February most masks were sold out in Portuguese pharmacies.


text: On 4 February, Marcelo Rebelo de Sousa, the President of the Portuguese Republic, admitted that the epidemic of the new coronavirus in China "affects the economic activity of a very powerful economy and thus affects the world's economic activity or could affect". He also admitted the possibility of economic upheavals due to the break in production."


text: An ongoing economic crisis in Turkey was exacerbated by the COVID-19 pandemic. Sale of Turkish goods worldwide fell due to the global economic slowdown. President Recep Tayyip Erdoğan cut interest rates in late 2021 in response to a surge in inflation of the Turkish lira.


text: On 13 February, heavy equipment manufacturer JCB announced its plan to reduce working hours and production due to shortages in their supply chain caused by the outbreak.


text: On 5 March, British airline Flybe finally collapsed into administration with the loss of 2,000 jobs after failing to secure financial support. The airline said the impact of the coronavirus pandemic is partly to blame for its collapse. Flybe provided more than half of UK domestic flights outside London.


text: During the pandemic, exports of many food and drink products from the UK declined significantly, and that included Scotch whisky. Distillers were required to close for some time and the hospitality industry worldwide experienced a major slump. According to news reports in February 2021, the Scotch whisky sector had experienced £1.1 billion in lost sales. A BBC News headline on 12 February 2021 summarized the situation: "Scotch whisky exports slump to 'lowest in a decade'".


text: Tourism in the UK (by visitors from both the UK and from other countries) declined substantially due to travel restrictions and lockdowns. For much of 2020, and into 2021, vacation travel was not permitted and entry into the UK was very strictly limited. Business travel, for example, declined by nearly 90% over previous years.


text: On 4 March, Canadian Prime Minister Justin Trudeau announced the creation of a new cabinet committee to manage the federal response to the coronavirus disease. A week later, on 11 March, the government announced a billion COVID-19 Response Fund that included a $50 million contribution to the World Health Organization and an additional $275 million to fund coronavirus research in Canada.


text: On 13 March, the Bank of Canada lowered the overnight rate target by 50 basis points to 0.75 percent in an unscheduled rate decision citing the "negative shocks to Canada's economy arising from the COVID-19 pandemic and the recent sharp drop in oil prices." In June 2020, Canada lost its triple "A" credit rating.


text: The National Institute of Statistics and Geography (INEGI) said the unemployment rate in Mexico increased from 3.6% in January 2020 to 3.7% in February 2020. The informal sector increased to 56.3% in February compared to 56.0% in February 2019. Fewer than half of Mexicans have paid sick leave or health care. BBVA México predicted a 4.5% economic contraction in 2020, while analysts at Capital Economics in London argued that the government had to do more to support the economy. They forecast a 6% contraction in 2020. HR Ratings, Latin America's first credit rating agency, said that the performance of the economy would depend on the government's response to the COVID-19 crisis.


text: The Mexican Stock Exchange fell to a record low on 10 March due to fears of the coronavirus and because of falling oil prices. The Bank of Mexico (Banxico) stepped in to prop up the value of the peso, which fell 14%. World markets are seeing falls similar to those of 1987.


text: The "Consejo Nacional Empresarial Turístico" (National Tourism Business Council, CNET) sent two letters in March to Alfonso Romo, Chief of Staff to the President of Mexico, outlining the importance of tourism to the economy and asking for government support for the sector. Tourism provides 4 million jobs in Mexico, and 93% of the companies have ten or fewer employees. COVID-19 forced the closure of 4,000 hotels (52,400 rooms) and 2,000 restaurants, while the airline industry lost MXN $30 billion (US$1.3 billion) through March. The association of car dealers, ADMA, predicted a decrease in domestic sales between 16% and 25% in 2020.


text: The viral outbreak was cited by many companies in their briefings to shareholders, but several maintained confidence that they would not be too adversely affected by short-term disruption due to "limited" exposure to the Chinese consumer market. Those with manufacturing lines in mainland China warned about possible exposure to supply shortages, while others cautioned that large corporations and the wealthy could exploit the crisis for economic gain in line with the Shock Doctrine, as has occurred after past pandemics


text: Silicon Valley representatives expressed worries about serious disruption to production lines, as much of the technology sector relies on factories in mainland China. Since there had been a scheduled holiday over Lunar New Year, the full effects of the outbreak on the tech sector were considered to be unknown , according to "The Wall Street Journal".


text: Cities with high populations of Chinese residents have seen an increase in demand for face masks to protect against the virus; many are purchasing masks to mail to relatives in mainland China, Hong Kong, and Macau, where there is a shortage of masks. , many stores in the United States had sold out of masks. This mask shortage has caused an increase in prices.


text: Universities in the United States have warned about a significant impact on their income due to a large number of Chinese international students potentially unable to attend classes.


text: "The Washington Post" reported in February that President Donald Trump told advisors that he did not want the government to say or do anything that might spook the stock market, on concerns a large-scale outbreak could hurt his reelection chances.


text: On 26 February, "The New York Times" (NYT) reported a case in California which the Center for Disease Control confirmed as the first possible community transmission of coronavirus in the United States.


text: On 27 February, the NYT reported delay in diagnosis of the community transmission case in California. A later article in the NYT on 27 February discussed a whistleblower's allegation's of the ineptitude of preparedness at Travis Air Force Base near Fairfield, California and March Air Reserve Base in Riverside County, California to receive possible coronavirus transmitters for diagnosis and treatment. The same day, a report by Goldman Sachs forecast that it believes American companies "will generate no earnings growth in 2020," wiping out an earnings recovery that was expected for the year after "lackluster profit reports for most of 2019"


text: On 27 February, U.S. stocks were on their way to the largest loss for a week since 2008, and the Dow Jones Industrial Average fell 1190 points in one day. On 28 February the average dropped below 25000 briefly. The Dow Jones ended the week down 12.4 percent, the S&P 500 Index 11.5 percent, and the Nasdaq Composite down 10.5 percent. Stocks fell to 18,592 points (Dow average) on 23 March after a procedural Senate vote on a coronavirus economic stimulus bill failed for the second time in two days.


text: On 7 March, US stocks fell by 7 percent, triggering a temporary halt in trading, which was also aided by the 2020 Russia–Saudi Arabia oil price war.


text: On the evening of 11 March, the National Basketball Association announced that the rest of its season would be suspended indefinitely, and the National Collegiate Athletic Association (NCAA) announced that its men's and women's basketball tournaments would be played without fans. The following day, the NCAA initially announced that it would cancel the basketball tournaments, but later that day announced that all championship events throughout all sports would be cancelled until 2020–21.


text: Deep South states such as Alabama, Georgia, and Louisiana reported on April6 that 70% of its reported deaths had involved African Americans. It has been acknowledged that African Americans were more likely to have poor living conditions (including dense urban environments and poverty), employment instability, chronic comorbidities influenced by these conditions, and little to no health insurance coverage—factors which can all exacerbate its impact.


text: In April, nearly a quarter of residents (renters and homeowners) did not pay full housing costs. Some did not pay rent/mortgage at all, while others did not make full payment. The difficulties experienced by many tenants during the pandemic have sparked a movement to cancel rent, which is advocated by some activists, organizations, and politicians.


text: According to the US Bureau of Labor Statistics, male unemployment increased sharply from 3.55 million in February to 11 million in April 2020, while female unemployment (lower than the pre-crisis men's) rose from 2.7 million to 11.5 million in the same period.


text: In early May, a Washington Post-Ipsos poll revealed racial disparities between adult workers who were laid off or furloughed since the beginning of the outbreak: layoffs affected 20 percent of Hispanic workers, 16 percent of black workers, 11 percent of white workers, and 12 percent of workers of other races.


text: Many workers were furloughed or laid off as a result of business and school closures and the cancellation of public events. During April more than 20 million Americans filed for unemployment insurance, an all-time record, and the national unemployment rate was reported as 14.7% – the highest monthly rate since record keeping was begun in 1948. The rise in unemployment may have contributed to protracted nationwide civil unrest.


text: For first quarter 2020, health care spending dropped 18 percent. 42,000 health care workers lost their jobs in March, and 1.4 million in April, as most hospitals postponed non-essential procedures. People who were left ended up doing the jobs of others who were furloughed.


text: Although the United States government is the world's largest borrower, credit card debt in the country fell below $1 trillion in May 2020 for the first time since May 2011, declining for the previous three months. This was due to a decrease in both personal income and disposible personal income while personal savings rates nearly doubled. A job reports validated the decline after indicating that three million jobs were added in June 2020, compared to the 20 million jobs lost throughout the pandemic.


text: In a "Business Economics" article that was published on 7 December 2020 and won NABE's 2020 Edmund A. Mennis Contributed Paper Award, Xiaobing Shu, Christine Chmura & James Stinchcomb claimed that "COVID-19 has caused a significant decline in labor demand, by as much as 30%, measured by the number of job advertisements. But the pandemic did not result in noticeable changes in advertised wages."


text: In December 2020, economist David Choi at Goldman Sachs argued that the U.S. economy would recover faster than expected as impact on the parts of the economy most susceptible to the recent coronavirus spread weren't being affected as severely. On the flipside, Alejandra Grindal at Ned Davis Research, argued that the economy could get worse if the pandemic worsens prior to the deployment of vaccines in Q2 2021, after which the economy would see "a pretty sharp recovery not only in U.S. economic activity, but also global economic activity".


text: Nearly 20 million adults – 9 percent of all adults in the country – reported that their household sometimes or often didn't have enough to eat in the last seven days, according to Household Pulse Survey data collected 29 September – 11 October 2021. When asked why, 82 percent said they "couldn’t afford to buy more food," rather than (or in addition to) non-financial factors such as lack of transportation or safety concerns due to the pandemic.


text: Even consumers with jobs have stopped spending. Retail sales plunged 20 percent from February to April, with very large declines in categories like clothing and accessory stores (down 89 percent) and department stores (down 45 percent). The personal saving rate jumped to 33 percent in March from 8 percent in February.


text: Unemployment increased significantly in the United States during the COVID-19 pandemic. However, in the United States, most enterprises that adopted advanced digital technologies were able to avert worker reductions more significantly than firms who did not digitally adapt.


text: Latin American and Caribbean countries were already facing low economic growth before COVID-19, with the region averaging 0.4% of growth in 2019, due to what was described as "a vicious circle of low-quality jobs, deficient social protection and volatile incomes" with one out of five in the ages of 14–25 being unable to find a job. The economic impact caused by COVID-19 was exarcebated by many countries' lack of reserve funds for times of crisis. Between 35 and 50 million people in the region are expected to fall below the poverty line, which is set at US$5.60 per day. Exports have also been affected and many countries are expected to fall further into debt. The LAC region is experiencing the biggest contraction in the emerging markets and developing economies. The IMF World Economic Outlook has reported a GDP contraction of 8.1 per cent in Latin America in 2020. Unfortunately, since 2014, the region has been experiencing the weakest period of growth since 1950.


text: On 19 March, Argentina entered a nationwide lockdown. The Argentine government announced the extension of the lockdown, originally intended to end on 31 March until mid-April. On 10 April, President Alberto Fernández announced that the lockdown would be extended in major cities until 26 April.


text: In response to the economic halt, on 24 March, the executive decreed the payment of a one-time welfare benefit to the lowest earning self-employed taxpayers left with no sources of income in their household.


text: On 22 September, official reports showed a record 19% year-on-year drop in the GDP for the second quarter of 2020, the biggest drop in the country's history. Investment fell 38% from the previous year.


text: Two Brazilian banks predicted the deceleration of economic growth in China. UBS has reviewed its estimations from 6% to 5.9%, while Itaú stated a reduction to 5.8%.


text: A representative of some of the bigger Brazilian companies of the electronics sector, Eletros, stated that the current stock for the supply of components is enough for around 10 to 15 days.


text: The prices of soybeans, oil, and iron ore have been falling. These three goods represent 30%, 24% and 21% of the Brazilian exports to China, respectively.


text: Prior to the pandemic, average public debt in Africa was predicted to progressively drop. Instead, average net government debt increased by 2 percentage points in 2020, reaching 61% GDP. The surge in Sub-Saharan Africa was significantly greater, with over 6 percentage points on average. Countries are suffering increasing debt payment expenses as a result of this rising debt burden. Some countries have lost complete access to the global markets thus becoming reliant on relatively limited internal resources and concessional finance.


text: Microfinance services are provided by commercial banks, commercial and regulatory microfinance institutions, informal providers, and non-governmental organizations. One of the responses of Africa's microfinance institutions to the COVID-19 crisis was to increase reliance on digital channels to support borrowers.


text: The European Investment Bank, with the help of the Making Finance Work for Africa Partnership (MFW4A), conducted the Banking in Africa survey in early 2021. 78 banks in Sub-Saharan Africa were surveyed. The banks that took part control nearly 30% of the continent's assets. The results showed that almost two-thirds of the Banks surveyed tightened lending rules in 2020 – 2021. More than 80% expanded their restructuring or loan moratoriums.


text: According to the European Investment Bank's Banking in Africa study 2021, digital offerings by Sub-Saharan African banks are increasing, especially as a result of the COVID-19 pandemic. The majority of the banks polled said that the pandemic has accelerated the speed of digital transformation, and that this change is permanent. 89% of the banks polled claimed that the pandemic has hastened the digital transformation of their internal operations; the same percentage believes that the consumer movement toward digital channels will continue once the virus has ended. Few banks were required to modify their employee levels, while slightly under one-third adjusted their prices. Approximately half of the answering banks had employed guarantees, the majority of which came from the central bank, the government, or an international financial institution. During the first half of 2020, the cost of overseas borrowing climbed dramatically. However, at the beginning of the pandemic, banks were well capitalized, thus they were able to resist liquidity challenges.


text: Around 88% of enterprises in countries where COVID-19 follow-up surveys were conducted (three in Southern Africa, one in East Africa, four in West Africa, and one in North Africa) were suffering diminished liquidity, with more than 55% of them closing temporarily during the COVID-19 pandemic. Almost 8% had declared bankruptcy, and 26% of enterprises are past due on financial institution commitments. Firms that depend on equity are at 36%. rather than depending on commercial bank loans to address cash flow issues, these are more likely to succeed at 16%.


text: The International Monetary Fund predicts that average growth in the African continent would return to 4.5% in 2021 and 4.0% in 2022. All economies except the Comoros are expected to increase in 2021. However, large differences in growth rates are expected, between 0.2% in the Republic of the Congo and 7.6% in Kenya in 2021.


text: Australia is expected to be heavily affected by the epidemic, with early estimations have GDP contracting by 0.2% to 0.5% and more than 20,000 Australian jobs being lost. The Australian Treasurer, Josh Frydenberg said that the country would no longer be able to promise a budget surplus due to the outbreak. The Australian dollar dropped to its lowest value since the Great Recession.


text: The Australasian College for Emergency Medicine called for a calm and a fact-based response to the epidemic, asking people to avoid racism, "panic and division" and the spread of misinformation. A large amount of protective face masks were purchased by foreign and domestic buyers, which has sparked a nationwide face masks shortage. In response to price increases of nearly 2000%, the Pharmaceutical Society of Australia has called on these "unethical suppliers" to keep supplies affordable.


text: Tourism bodies have suggested that the total economic cost to the sector, as of 11 February 2020, would be A$4.5 billion. Casino earnings are expected to fall. At least two localities in Australia, Cairns and the Gold Coast, have reported already lost earnings of more that $600 million. The Australian Tourism Industry Council (ATIC) called on the Government of Australia for financial support especially in light of the large number of small businesses affected.


text: Mining companies are thought to be highly exposed to the outbreak, since sales to China constitute 93% of the sales of Fortescue Metals, 55% of the sales of BHP, and 45% of the sales of Rio Tinto. The iron ore shipping gauge dropped 99.9% as a result of the outbreak, and the virus has made shipping and logistic operations of mining companies more complicated.


text: Agriculture is also experiencing negative effects from the outbreak, including the Australian dairy industry, fishing industry, wine producers, and meat producers. On 13 February 2020, Rabobank, which specialises in agricultural banking, warned that the agricultural sector had eight weeks for the coronavirus to be contained before facing major losses. Exports were also affected by the outbreak. In May, China—which is Australia's largest trading partner—stopped accepting Australian meat and placed tariffs on Australian barley, likely a punitive response to Australia's call for an investigation into the origin of the global pandemic.


text: The education sector is expected to suffer a US$5 billion loss according to an early government estimate, including costs due to "tuition fee refunds, free deferral of study, realignment of teaching calendars and student accommodation costs." The taxpayer is likely to be required to cover the shortfall in education budgets. An estimated 100,000 students were not able to enroll at the start of the semester. Nearly two-thirds of Chinese students were forced to remain overseas due to visa restrictions on travellers from mainland China. Salvatore Babones, associate professor at the University of Sydney, stated that "Australia will remain an attractive study destination for Chinese students, but it may take several years for Chinese student numbers to recover".


title: SNCF

text: The Société nationale des chemins de fer français (; abbreviated as SNCF ; French for "National society of French railroads") is France's national state-owned railway company. Founded in 1938, it operates the country's national rail traffic along with Monaco, including the TGV, on France's high-speed rail network. Its functions include operation of railway services for passengers and freight (through its subsidiaries SNCF Voyageurs and Rail Logistics Europe), as well as maintenance and signalling of rail infrastructure (SNCF Réseau). The railway network consists of about of route, of which are high-speed lines and electrified. About 14,000 trains are operated daily.


title: SNCF

text: In 2010 the SNCF was ranked 22nd in France and 214th globally on the Fortune Global 500 list. It is the main business of the SNCF Group, which in 2020 had €30 billion of sales in 120 countries. The SNCF Group employs more than 275,000 employees in France and around the world. Since July 2013, the SNCF Group headquarters are located in a Parisian suburb at 2 Place aux Étoiles in Saint-Denis. The president of SNCF Group has been since 2019.


title: SNCF

text: SNCF operates almost all of France's railway traffic, including the TGV ("Train à Grande Vitesse", meaning "high-speed train"). In the 1970s, the SNCF began the TGV high-speed train program with the intention of creating the world's fastest railway network. It came to fruition in 1981 with the completion of the first high-speed line LGV Sud-Est ("Ligne à Grande Vitesse Sud-Est", meaning "southeast high-speed line"), where the first TGV service, from Paris to Lyon, was inaugurated. In 2017, the national rail network owned by SNCF Réseau had 28,710 km (17,839 mi) of lines, 58% of which were electrified and 2,640 high-speed lines. Every day, the SNCF runs 15,000 commercial trains and transports more than 5 million passengers and more than 250,000 tonnes of goods. TGV lines and TGV technology are now spread across several European countries.


title: SNCF

text: The SNCF's TGV has set many world speed records, the most recent on 3 April 2007, when a new version of the TGV dubbed the V150 with larger wheels than the usual TGV, was able to cover more ground with each rotation and had a stronger engine, and broke the world speed record for conventional railway trains, reaching .


title: SNCF

text: The SNCF has a remarkable safety record. After nearly 30 years in operation, SNCF's TGV system has only experienced one fatal accident, which occurred during pre-opening testing and not in regular operation.


title: SNCF

text: In 2011 SNCF in partnership with Keolis, unsuccessfully bid for the InterCity West Coast franchise. In April 2017 SNCF took a 30% shareholding in a joint venture with Stagecoach Group and Virgin Group to bid for the West Coast Partnership that will operate services on the West Coast Main Line from May 2020 and the High Speed 2 line from 2026.


title: SNCF

text: In April 2019 Stagecoach were banned from bidding for any franchises including the West Coast Partnership which has meant that Virgin and SNCF have now had to withdraw from the shortlist.


title: SNCF

text: Since the 1990s, SNCF has been selling railway carriages to regional governments, with the creation of the Train Express Régional brand. SNCF also maintains a broad scope of international business that includes work on freight lines, inter-city lines and commuter lines. SNCF experts provide logistics, design, construction, operations and maintenance services. SNCF operates the international ticketing agency Oui.sncf, formerly Voyages-sncf.com and Rail Europe.


title: SNCF

text: SNCF has employees in 120 countries offering extensive overseas and cross border consulting. Those projects include:


title: SNCF

text: SNCF was formed in 1938 with the nationalisation of France's main railway companies ("Chemin de fer", literally, 'way of iron', means railway). These were the:


title: SNCF

text: The French state originally took 51% ownership of SNCF and invested large amounts of public subsidies into the system. Today, SNCF is wholly owned by the French state.


title: SNCF

text: Following the 1940 Armistice and until August 1944, SNCF was requisitioned for the transport of German armed forces and armaments. The invading German troops were responsible for the destruction of nearly 350 French railway bridges and tunnels. According to differing estimates, SNCF surrendered between 125,000 and 213,000 wagons and 1,000-2,000 locomotives.


title: SNCF

text: France's railway infrastructure and rolling stocks were a target for the French Resistance aimed at disrupting and fighting the German occupying forces. This allowed SNCF employees to perform many acts of resistance, including the formation of the Résistance-Fer movement in 1943. Nearly 1,700 SNCF railway workers were killed or deported for resisting Nazi orders. 150 Résistance-Fer agents were shot for their acts of resistance, 500 of them were deported. Half of those deported died in concentration camps.


title: SNCF

text: German occupying forces in France also requisitioned SNCF to transport nearly 77,000 Jews and other Holocaust victims to Nazi extermination camps. These deportations have been the subject of historical controversy and lawsuits (such as the Lipietz case) in France as well as in the United States (where subsidiary Keolis is a transportation contractor) to the present day.


title: SNCF

text: In 1992 SNCF commissioned French academics to write a history of SNCF activities during World War II. The resultant report was published in 1996.


title: SNCF

text: More recently, some sources have claimed that SNCF billed Nazi-occupied France for third-class tickets for Holocaust victims transported to extermination camps, although passengers were transported in cattle cars. Other sources have reported that after the liberation of France SNCF continued to seek payment for transporting Holocaust victims to Germany. However, historian Michael Marrus has written that claims that SNCF billed for third-class tickets and continued to seek payment after the war ended were made as part of a legal case brought against SNCF, and did not match with historians' understanding of what happened. Marrus argues that SNCF had no margin of maneuver during the German occupation and that the actions of SNCF employees were not ideologically motivated. According to Serge Klarsfeld, president of the organization Sons and Daughters of Jewish Deportees from France, SNCF was forced by German and Vichy authorities to cooperate in providing transport for French Jews to the border and did not make any profit from this transport.


title: SNCF

text: In December 2014, SNCF agreed to pay up to $60 million worth of compensation to Holocaust survivors in the United States. It corresponds to approximately $100,000 per survivor.


title: SNCF

text: In the early 2000s, SNCF sought to get a contract from the state of California for a bullet train project between Los Angeles and San Francisco. SNCF recommended that the train take the most direct route between the two locations to reduce the complexity and cost of the project, but the SNCF's recommendations were cast aside by California politicians who wanted to divert the train through various communities, raising the cost and complexity of the project, as well as the expected travel time. SNCF pulled out of the project in 2011 and went to Morocco to help the country construct a bullet train service. By 2018, Morocco's bullet train started service while the California bullet train project was not close to being operational in 2022, with some saying that the project would never be completed.


title: SNCF

text: In May 2014, the company had discovered that 2,000 new trains they ordered at a cost of 15 billion euros are too wide for many of France's regional platforms. Construction work has started to reconfigure them.


title: SNCF

text: On 1 January 2015, Réseau ferré de France (RFF) merged with SNCF Infra and the Direction de la circulation ferroviaire (DCF) and became "SNCF Réseau", the operational assets of SNCF became "SNCF Mobilités", and both groups were placed under the control of SNCF.


title: SNCF

text: The industrial designer Paul Arzens styled many of SNCF's locomotives from the 1940s until the 1970s. A particularly distinctive type is the "broken nose" style of electric and diesel locomotives.


title: SNCF

text: SNCF codeshares with Air Austral, Air France, Air Tahiti Nui, American Airlines, Cathay Pacific, Middle East Airlines, Etihad Airways, Qatar Airways, and SriLankan Airlines. In exchange, SNCF allows passengers on these flights to book railway services between Charles de Gaulle Airport in Roissy (near Paris) and Aix-en-Provence, Angers, Avignon, Bordeaux, Le Mans, Lille, Lyon Part-Dieu, Marseille, Montpellier, Nantes, Nîmes, Poitiers, Rennes, Strasbourg, Tours, and Valence with their airline. The IATA designator used by airlines in connection with these journeys is 2C.


title: SNCF

text: Until 1999, the SNCF's historic headquarters was located at 88 Rue Saint-Lazare in the 9th arrondissement. In 1996 the chairman of SNCF, Louis Gallois, announced that SNCF would move its headquarters to a new location during the middle of 1997.


title: SNCF

text: From 1999 to 2013, SNCF's headquarters were located in the Montparnasse neighborhood of the 14th arrondissement of Paris, located near the Gare Montparnasse.


title: SNCF

text: Since July 2013, the SNCF headquarters are located in the Parisian suburb of Saint-Denis at 2, place aux Étoiles, 93200 Saint Denis. The move was motivated by cutting operating costs by 10 million euros per year.


title: SNCF

text: Since 1 January 2020 SNCF is a state-owned group consisting of a parent company (SNCF) with several independently operated subsidiaries:


title: SNCF

text: SNCF has full or partial shares in a large number of companies, the majority of which are rail or transport related. These include:


title: SNCF

text: According to a TNS SOFRES survey published in 2010, 66% of French people have a good image of SNCF. At the end of 2019, this proportion was measured at 50% by the Posternak-Ifop barometer on the image of companies. In 2020, Eight Advisory and IFOP unveil their ranking of the "most admired French companies": SNCF is in 23rd position.


title: SNCF

text: Safety on trains is also often a priority. To do this, around 2,800 railway workers form the Railway Security, the general supervision of SNCF, of which 50% of the workforce is assigned to the Île-de-France region.


title: SNCF

text: Furthermore, the experts of the BCG, Boston Consulting Group , use to compare the rail systems in 25 European countries. They rank France in tied 4th position (with Germany, Austria and Sweden), behind Switzerland, Denmark and Finland. The criteria are : the utilization rate, quality of service and safety.


title: SNCF

text: SNCF's current visual logo was created in 2005 by the Carré Noir agency, a subsidiary of the Publicis communication group. It was slightly reworked in 2011: rounded corners, disappearance of shadows inside the letters as well as behind, and a clearer separation between them.


title: SNCF

text: The SNCF sound logo - the four notes C - G - A flat - E flat -, in a sung version, was created in 2005 by Michaël Boumendil. David Gilmour, guitarist of the group Pink Floyd, used the jingle as the inspiration for the title track of his 2015 album "Rattle That Lock". Simone Hérault has been the voice of SNCF since 1981


title: SNCF

text: Since the Auguste and Louis Lumière's first film, SNCF has been the company that hosts the most film shoots in France, between 50 and 60 shoots per year, which represents around two thirds of French productions. A selection of iconic films where SNCF is at the heart of the matter include:


title: Σ-algebra

text: In mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set "X" is a nonempty collection Σ of subsets of "X" closed under complement, countable unions, and countable intersections. The pair ("X", Σ) is called a measurable space.


title: Σ-algebra

text: The σ-algebras are a subset of the set algebras; elements of the latter only need to be closed under the union or intersection of "finitely" many subsets, which is a weaker condition.


title: Σ-algebra

text: The main use of σ-algebras is in the definition of measures; specifically, the collection of those subsets for which a given measure is defined is necessarily a σ-algebra. This concept is important in mathematical analysis as the foundation for Lebesgue integration, and in probability theory, where it is interpreted as the collection of events which can be assigned probabilities. Also, in probability, σ-algebras are pivotal in the definition of conditional expectation.


title: Σ-algebra

text: In statistics, (sub) σ-algebras are needed for the formal mathematical definition of a sufficient statistic, particularly when the statistic is a function or a random process and the notion of conditional density is not applicable.


title: Σ-algebra

text: If one possible σ-algebra on "X" is where ∅ is the empty set. In general, a finite algebra is always a σ-algebra.


title: Σ-algebra

text: If {"A", "A", "A", …} is a countable partition of "X" then the collection of all unions of sets in the partition (including the empty set) is a σ-algebra.


title: Σ-algebra

text: A more useful example is the set of subsets of the real line formed by starting with all open intervals and adding in all countable unions, countable intersections, and relative complements and continuing this process (by transfinite iteration through all countable ordinals) until the relevant closure properties are achieved (a construction known as the Borel hierarchy).


title: Σ-algebra

text: There are at least three key motivators for σ-algebras: defining measures, manipulating limits of sets, and managing partial information characterized by sets.


title: Σ-algebra

text: A measure on "X" is a function that assigns a non-negative real number to subsets of "X"; this can be thought of as making precise a notion of "size" or "volume" for sets. We want the size of the union of disjoint sets to be the sum of their individual sizes, even for an infinite sequence of disjoint sets.


title: Σ-algebra

text: One would like to assign a size to "every" subset of "X", but in many natural settings, this is not possible. For example, the axiom of choice implies that when the size under consideration is the ordinary notion of length for subsets of the real line, then there exist sets for which no size exists, for example, the Vitali sets. For this reason, one considers instead a smaller collection of privileged subsets of "X". These subsets will be called the measurable sets. They are closed under operations that one would expect for measurable sets, that is, the complement of a measurable set is a measurable set and the countable union of measurable sets is a measurable set. Non-empty collections of sets with these properties are called σ-algebras.


title: Σ-algebra

text: Many uses of measure, such as the probability concept of almost sure convergence, involve limits of sequences of sets. For this, closure under countable unions and intersections is paramount. Set limits are defined as follows on σ-algebras.


title: Σ-algebra

text: In much of probability, especially when conditional expectation is involved, one is concerned with sets that represent only part of all the possible information that can be observed. This partial information can be characterized with a smaller σ-algebra which is a subset of the principal σ-algebra; it consists of the collection of subsets relevant only to and determined only by the partial information. A simple example suffices to illustrate this idea.


title: Σ-algebra

text: Imagine you and another person are betting on a game that involves flipping a coin repeatedly and observing whether it comes up Heads ("H") or Tails ("T"). Since you and your opponent are each infinitely wealthy, there is no limit to how long the game can last. This means the sample space Ω must consist of all possible infinite sequences of "H" or "T":


title: Σ-algebra

text: However, after "n" flips of the coin, you may want to determine or revise your betting strategy in advance of the next flip. The observed information at that point can be described in terms of the 2 possibilities for the first "n" flips. Formally, since you need to use subsets of Ω, this is codified as the σ-algebra


title: Σ-algebra

text: Let "X" be some set, and let formula_9 represent its power set. Then a subset formula_10 is called a "σ"-algebra if it satisfies the following three properties:


title: Σ-algebra

text: From these properties, it follows that the σ-algebra is also closed under countable intersections (by applying De Morgan's laws).


title: Σ-algebra

text: It also follows that the empty set ∅ is in Σ, since by (1) "X" is in Σ and (2) asserts that its complement, the empty set, is also in Σ. Moreover, since } satisfies condition (3) as well, it follows that } is the smallest possible σ-algebra on "X". The largest possible σ-algebra on "X" is formula_9.


title: Σ-algebra

text: Elements of the "σ"-algebra are called measurable sets. An ordered pair , where "X" is a set and Σ is a "σ"-algebra over "X", is called a measurable space. A function between two measurable spaces is called a measurable function if the preimage of every measurable set is measurable. The collection of measurable spaces forms a category, with the measurable functions as morphisms. Measures are defined as certain types of functions from a "σ"-algebra to [0, ∞].


title: Σ-algebra

text: A σ-algebra is both a π-system and a Dynkin system (λ-system). The converse is true as well, by Dynkin's theorem (below).


title: Σ-algebra

text: This theorem (or the related monotone class theorem) is an essential tool for proving many results about properties of specific σ-algebras. It capitalizes on the nature of two simpler classes of sets, namely the following.


title: Σ-algebra

text: Dynkin's π-λ theorem says, if "P" is a π-system and "D" is a Dynkin system that contains "P", then the σ-algebra σ("P") generated by "P" is contained in "D". Since certain π-systems are relatively simple classes, it may not be hard to verify that all sets in "P" enjoy the property under consideration while, on the other hand, showing that the collection "D" of all subsets with the property is a Dynkin system can also be straightforward. Dynkin's π-λ Theorem then implies that all sets in σ("P") enjoy the property, avoiding the task of checking it for an arbitrary set in σ("P").


title: Σ-algebra

text: One of the most fundamental uses of the π-λ theorem is to show equivalence of separately defined measures or integrals. For example, it is used to equate a probability for a random variable "X" with the Lebesgue-Stieltjes integral typically associated with computing the probability:


title: Σ-algebra

text: where "F"("x") is the cumulative distribution function for "X", defined on R, while formula_13 is a probability measure, defined on a σ-algebra Σ of subsets of some sample space Ω.


title: Σ-algebra

text: A "σ"-algebra Σ is just a "σ"-ring that contains the universal set "X". A "σ"-ring need not be a "σ"-algebra, as for example measurable subsets of zero Lebesgue measure in the real line are a "σ"-ring, but not a "σ"-algebra since the real line has infinite measure and thus cannot be obtained by their countable union. If, instead of zero measure, one takes measurable subsets of finite Lebesgue measure, those are a ring but not a "σ"-ring, since the real line can be obtained by their countable union yet its measure is not finite.


title: Σ-algebra

text: "σ"-algebras are sometimes denoted using calligraphic capital letters, or the Fraktur typeface. Thus may be denoted as formula_23 or formula_24.


title: Σ-algebra

text: A separable σ-algebra (or separable σ-field) is a σ-algebra formula_25 that is a separable space when considered as a metric space with metric formula_26 for formula_27 and a given measure formula_28 (and with formula_29 being the symmetric difference operator). Note that any σ-algebra generated by a countable collection of sets is separable, but the converse need not hold. For example, the Lebesgue σ-algebra is separable (since every Lebesgue measurable set is equivalent to some Borel set) but not countably generated (since its cardinality is higher than continuum).


title: Σ-algebra

text: A separable measure space has a natural pseudometric that renders it separable as a pseudometric space. The distance between two sets is defined as the measure of the symmetric difference of the two sets. Note that the symmetric difference of two distinct sets can have measure zero; hence the pseudometric as defined above need not to be a true metric. However, if sets whose symmetric difference has measure zero are identified into a single equivalence class, the resulting quotient set can be properly metrized by the induced metric. If the measure space is separable, it can be shown that the corresponding metric space is, too.


title: Σ-algebra

text: so-called , which in a filtered probability space describes the information up to the random time formula_30 in the sense that, if the filtered probability space is interpreted as a random experiment, the maximum information that can be found out about the experiment from arbitrarily often repeating it until the time formula_30 is formula_32.


title: Σ-algebra

text: Let "F" be an arbitrary family of subsets of "X". Then there exists a unique smallest σ-algebra which contains every set in "F" (even though "F" may or may not itself be a σ-algebra). It is, in fact, the intersection of all σ-algebras containing "F". (See intersections of σ-algebras above.) This σ-algebra is denoted σ("F") and is called the σ-algebra generated by "F".


title: Σ-algebra

text: If "F" is empty, then σ("F")=}. Otherwise σ("F") consists of all the subsets of "X" that can be made from elements of "F" by a countable number of complement, union and intersection operations.


title: Σ-algebra

text: For a simple example, consider the set "X" = {1, 2, 3}. Then the σ-algebra generated by the single subset {1} is </nowiki>}}. By an abuse of notation, when a collection of subsets contains only one element, "A", one may write σ("A") instead of σ({"A"}); in the prior example σ({1}) instead of σ(<nowiki></nowiki>). Indeed, using to mean is also quite common.


title: Σ-algebra

text: There are many families of subsets that generate useful σ-algebras. Some of these are presented here.


title: Σ-algebra

text: If formula_36 is a function from a set formula_37 to a set formula_38 and formula_39 is a formula_31-algebra of subsets of formula_38, then the formula_31-algebra generated by the function formula_36, denoted by formula_44, is the collection of all inverse images formula_45 of the sets formula_46 in formula_39. i.e.


title: Σ-algebra

text: A function "f" from a set "X" to a set "Y" is measurable with respect to a σ-algebra Σ of subsets of "X" if and only if σ("f") is a subset of Σ.


title: Σ-algebra

text: One common situation, and understood by default if "B" is not specified explicitly, is when "Y" is a metric or topological space and "B" is the collection of Borel sets on "Y".


title: Σ-algebra

text: If "f" is a function from "X" to R then σ("f") is generated by the family of subsets which are inverse images of intervals/rectangles in R:


title: Σ-algebra

text: A useful property is the following. Assume "f" is a measurable map from ("X", Σ) to ("S", Σ) and "g" is a measurable map from ("X", Σ) to ("T", Σ). If there exists a measurable map "h" from ("T", Σ) to ("S", Σ) such that "f"("x") = "h"("g"("x")) for all "x", then σ("f") ⊂ σ("g"). If "S" is finite or countably infinite or, more generally, ("S", Σ) is a standard Borel space (e.g., a separable complete metric space with its associated Borel sets), then the converse is also true. Examples of standard Borel spaces include R with its Borel sets and R with the cylinder σ-algebra described below.


title: Σ-algebra

text: An important example is the Borel algebra over any topological space: the σ-algebra generated by the open sets (or, equivalently, by the closed sets). Note that this σ-algebra is not, in general, the whole power set. For a non-trivial example that is not a Borel set, see the Vitali set or Non-Borel sets.


title: Σ-algebra

text: On the Euclidean space R, another σ-algebra is of importance: that of all Lebesgue measurable sets. This σ-algebra contains more sets than the Borel σ-algebra on R and is preferred in integration theory, as it gives a complete measure space.


title: Σ-algebra

text: Let formula_50 and formula_51 be two measurable spaces. The σ-algebra for the corresponding product space formula_52 is called the product σ-algebra and is defined by


title: Σ-algebra

text: The Borel σ-algebra for R is generated by half-infinite rectangles and by finite rectangles. For example,


title: Σ-algebra

text: is a set of real-valued functions. Let formula_57 denote the Borel subsets of R. A cylinder subset of is a finitely restricted set defined as


title: Σ-algebra

text: is an algebra that generates the cylinder σ-algebra for . This σ-algebra is a subalgebra of the Borel σ-algebra determined by the product topology of formula_62 restricted to .


title: Σ-algebra

text: An important special case is when formula_63 is the set of natural numbers and is a set of real-valued sequences. In this case, it suffices to consider the cylinder sets


title: Σ-algebra

text: Suppose formula_66 is a probability space. If formula_67 is measurable with respect to the Borel σ-algebra on R then is called a random variable ("n = 1") or random vector ("n" > 1). The σ-algebra generated by is


title: Σ-algebra

text: Suppose formula_66 is a probability space and formula_70 is the set of real-valued functions on formula_63. If formula_72 is measurable with respect to the cylinder σ-algebra formula_73 (see above) for then is called a stochastic process or random process. The σ-algebra generated by is


title: Dancing on Ice

text: Dancing on Ice is a British television series presented by Phillip Schofield alongside Holly Willoughby from 2006 to 2011, who then returned in 2018, and Christine Bleakley from 2012 to 2014. The series features celebrities and their professional partners figure skating in front of a panel of judges. The series, broadcast on ITV, started on 14 January 2006 and ended on 9 March 2014 after the contract was not renewed by ITV.


title: Dancing on Ice

text: On 4 September 2017, it was announced that a revived series would air on ITV from 7 January 2018 with Schofield and Willoughby returning as hosts. Jayne Torvill and Christopher Dean assumed new roles as head judges, alongside original judge Jason Gardiner and new judge Ashley Banjo. In 2020, John Barrowman replaced Gardiner as a judge, however on 3 October 2021, it was announced that Barrowman would not be returning to the judging panel. His replacement was later announced as "Strictly Come Dancing" professional Oti Mabuse. During the finale of the fourteenth series, it was confirmed that the show would return in 2023 for its fifteenth series.


title: Dancing on Ice

text: The series was announced in November 2004 and originally titled "Stars on Thin Ice", the show was renamed following the failure of ITV's celebrity oriented 2005 summer schedule. "Dancing on Ice" is frequently compared to the BBC's "Strictly Come Dancing". In 2004, the BBC aired a "Strictly" special entitled "Strictly Ice Dancing at Christmas", which was won by England goalkeeper David Seaman, who later became a contestant on the first series of "Dancing on Ice".


title: Dancing on Ice

text: ITV's show was given a January premiere amidst network doubts about its viability but became a surprise hit in Britain, where it became the third highest rated television show of 2006. It attained an impressive 13 million viewers for the final in March. Britain's best-known ice-skating duo and former Olympic champions Jayne Torvill and Christopher Dean help to train the aspiring dancers, and also appear throughout the show with comments and advice. Head Coach Karen Barber also trains the skaters for the live show. From the beginning, Torvill and Dean opened every episode with a performance, with the exception of the second, third and fourth shows of the fourth series, when Torvill performed alone due to Dean's recovery from a shoulder operation. From 2012, they performed less frequently.


title: Dancing on Ice

text: Schofield previously presented with Holly Willoughby, with commentary originally from Tony Gubba (later Simon Reed) and voiceovers done by John Sachs. The members of "The Ice Panel" were originally Karen Barber, Jason Gardiner, Nicky Slater and Robin Cousins, and the fifth judge varied from series to series: Karen Kresge in the first series, Natalia Bestemianova in the second, Ruthie Henshall in the third and fourth and Emma Bunton in the fifth. In series 6, there were only three judges: Gardiner, Cousins and Bunton.


title: Dancing on Ice

text: During the shows first two series, it ran two supplementary programmes – "Dancing on Ice Defrosted", presented by Stephen Mulhern, and "Dancing on Ice Exclusive" (or "Dancing on Ice Extra" during series 1) presented by Andi Peters alongside Andrea McLean in series 1 and Ben Shephard in series 2. In mid-2007, it was announced that both shows would not return to accompany the third series as the audience attracted was out of ITV2's target range. As part of ITV's new revamped schedule at the start of 2008, from the third series, the show aired on a Sunday night and featured updated music and new titles as well as redesigned graphics. The series 3 finale was a massive draw, pulling an average 11.7 million viewers (up from 9.6 million the previous year) peaking at 12.6 million viewers over the two-hour slot, up over a million from series 2.


title: Dancing on Ice

text: The seventh series began on 8 January 2012, with Torvill and Dean as coaches for which they will be paid £250,000 each series. Christine Bleakley was announced as the new co-presenter of the show replacing Holly Willoughby, whilst Katarina Witt and Louie Spence replaced Emma Bunton and Jason Gardiner on the judging panel. On 20 November 2012, it was announced that Gardiner was to return to the panel for the 2013 series, replacing Spence. The full judging panel for the 2013 series was revealed on 28 December 2012, with former The Pussycat Dolls singer Ashley Roberts joining and Karen Barber returning to the panel after acting as head coach on the show the previous two years; they joined Gardiner and head judge Robin Cousins on the panel.


title: Dancing on Ice

text: On 21 May 2013, Torvill and Dean announced that they would leave the series after its ninth series in 2014, leading to speculation that the whole show would be axed. On 24 June 2013 it was rumoured that "Dancing on Ice" may continue after they have left with new coaches, however, on 22 October 2013 it was confirmed that the show would end after its ninth series in 2014.


title: Dancing on Ice

text: On 4 September 2017, ITV confirmed that the show would return in 2018. Torvill and Dean will return to the show as head judges along with Schofield and Willoughby as presenters. On 19 October 2017, Ashley Banjo was confirmed as a judge. Later that month, Gardiner confirmed that he would return to the judging panel. Ashley's brother, Jordan Banjo, acts as the show's backstage digital host. ITV Racing's betting presenter Matt Chapman was announced as the new commentator on 16 December 2017. However, following the first live show on 7 January, Chapman claimed that he had "quit" the show but it was later confirmed to be a decision by the ITV producers, responding to pressure from the TV audience. Sportscaster Sam Matterface was later confirmed as Chapman's replacement. On 21 August 2019, Gardiner confirmed that he would not return for the 12th series in 2020. At the start of September, series one contestant John Barrowman was confirmed as his replacement. On 3 October 2021, ITV announced that Barrowman would not be returning to the judging panel in 2022. In December, it was confirmed that "Strictly Come Dancing" professional Oti Mabuse would replace him for the fourteenth series.


title: Dancing on Ice

text: Each week the celebrities and their partners perform a live ice dance routine. The four/five (as of Series 8) judges (commonly known as the Ice Panel) judge each performance and give a mark between 0.0 and 10.0 (0.0 to 6.0 between series 1 and 5), depending on the performance. These total scores then create a leaderboard which combines with the public vote in order to determine the two lowest placed couples. As this is the case, the pair with the lowest score from the judges can avoid being in the bottom two if the public vote for them.


title: Dancing on Ice

text: Once the scores and votes are combined to form the final leaderboard for that week's show, the two/three couples at the bottom compete in a final showdown known as the "Skate Off", where they perform a different routine known as the "Save-Me Skate". Unlike the main routines, this routine can be reused if the celebrity is in the Skate Off more than once. Once the couples have performed their routines for the judging panel, the judges decide on who deserves to stay and cast their votes, based on their second performance. The couple with the most votes from the judges receives a place in the following week's show, while the couple with the fewest votes leaves the competition. One couple leaves the competition each week, but in series 7, two couples left in one week, due to numbering issues. This also occurred in series 10, 11 and 14 respectively.


title: Dancing on Ice

text: A live reunion special was staged one week after the end of each season, with all celebrities talking about their experiences during the season, and answering questions from a live studio audience. Torvill and Dean themselves then made a special in-studio appearance towards the end, thanking the contestants, hosts and judges, and the viewers for their votes.


title: Dancing on Ice

text: From Series 1 to 8, there was an element that the skaters were required to perform as part of their routines. From Series 9, the required skating elements format was removed due to the All-Star nature of the series. It was brought back in Series 10, known as the "judges' challenge". The required elements included:


title: Dancing on Ice

text: The show was based in the George Lucas Stage at Elstree Studios from 2006 to 2010. In 2011 the show was broadcast from Shepperton Studios. In 2012 it returned to Elstree with a new, more modern set. There were several areas of the Elstree studio. "The Tunnel" was to the left of the rink and was where the couples entered the rink. "The Ice Cave" was situated at the back of the rink and was where Phillip Schofield and Torvill and Dean stood to interview the couples. "The Judges and Contestants Area" was to the right of the rink and was where the judging panel were based, and where Holly Willoughby or Christine Bleakley stood to speak to them and the couples.


title: Dancing on Ice

text: The first series began on Saturday 14 January 2006 and ended on Saturday 4 March 2006, including ten celebrity skaters. The co-presenters were Phillip Schofield and Holly Willoughby, while "The Ice Panel" consisted of one-time World Junior Figure Skating champion Nicky Slater, choreographer Karen Kresge, theatre producer Jason Gardiner, two-time NHK Trophy champion Karen Barber and 1980 Olympic champion Robin Cousins.


title: Dancing on Ice

text: The second series began on Saturday 20 January 2007. In it, 11 celebrities competed, compared to ten in the first series. The final was held on Saturday 17 March 2007. Phillip Schofield and Holly Willoughby returned to co-present, while Nicky Slater, Jason Gardiner, Karen Barber and Robin Cousins returned to "The Ice Panel". Karen Kresge did not return as a judge for a second series and was replaced by five-time European champion Natalia Bestemianova.


title: Dancing on Ice

text: The commissioning of the third series of "Dancing on Ice" was first confirmed by Phillip Schofield at the BAFTA awards.


title: Dancing on Ice

text: The third series began on 13 January 2008, moving to Sunday nights in the process and ended on 16 March 2008, when Suzanne Shaw was crowned as the winner. Schofield and Holly Willoughby returned to co-present, while Nicky Slater, Jason Gardiner and Robin Cousins returned to "The Ice Panel". The third series saw the replacement of judge Natalia Bestemianova by West End star Ruthie Henshall. And for the first time in the history of the series, a contestant withdrew due to injury, and it was TV presenter Michael Underwood who did so.


title: Dancing on Ice

text: The fourth series started on 11 January 2009 and ended on 22 March 2009. Phillip Schofield and Holly Willoughby returned to co-present as well as Jayne Torvill, Christopher Dean and Karen Barber to mentor the celebrities. Barber, Nicky Slater, Jason Gardiner, Robin Cousins and Ruthie Henshall all returned to "The Ice Panel" for the fourth series.


title: Dancing on Ice

text: The fifth series began on 10 January 2010 and ended on 28 March 2010. Jayne Torvill, Christopher Dean and Karen Barber returned to train the celebrities, with Phillip Schofield and Holly Willoughby returning as co-presenters. Barber, Nicky Slater, Jason Gardiner and Robin Cousins returned for their fifth series on "The Ice Panel". However, Ruthie Henshall did not return for her third series on "The Ice Panel" and was replaced by singer Emma Bunton. In addition to the main show, there was also a new spin-off show called "Dancing on Ice Friday" which gives viewers the insight to the training of the celebrities. It was presented by Ben Shephard and former contestant Coleen Nolan and broadcast from 8 pm to 8.30 pm on Friday evenings on ITV.


title: Dancing on Ice

text: Cousins did not appear as a judge for weeks 6 and 7 due to commentary commitments for the Winter Olympics, so Barber was temporary head judge during Cousins's absence. Michael Ball took his place on 14 February and Angela Rippon filled in for him on 21 February.


title: Dancing on Ice

text: The sixth series started on 9 January 2011 and ended on 27 March 2011 with the following 16 celebrities taking part. The first two episodes were qualifying rounds, in each of which eight couples skated and two were eliminated, so that only 12 couples reached the competition proper. For the first time, viewers in the Republic of Ireland were able to vote via the TV3 Ireland website. Christopher Dean and Jayne Torvill returned to mentor the contestants, with Karen Barber moving from "The Ice Panel" to the role of head coach. Phillip Schofield and Holly Willoughby returned as co-presenters for their sixth series. Jason Gardiner, Robin Cousins and Emma Bunton returned to "The Ice Panel", but Nicky Slater did not.


title: Dancing on Ice

text: The seventh series started on 8 January 2012. The celebrities were revealed on 3 January 2012. Phillip Schofield returned as presenter and was joined by Christine Bleakley following the departure of Holly Willoughby, with Christopher Dean, Jayne Torvill and Karen Barber returning to mentor the celebrities. Robin Cousins was the only judge from series 6 to return, with six consecutive European champion Katarina Witt and choreographer Louie Spence replacing Emma Bunton and Jason Gardiner.


title: Dancing on Ice

text: The contestants for the seventh series are as follows. Singer Chesney Hawkes was originally part of the line-up, but withdrew after sustaining an injury. His replacement was "The X Factor" contestant Chico.


title: Dancing on Ice

text: The line-up was officially announced on 18 December 2012. Consisting of twelve couples, series 8 was the shortest series to air, and had the lowest number of couples since series 3 in 2008.


title: Dancing on Ice

text: Christopher Dean, Jayne Torvill and Karen Barber returned to mentor the celebrities, with Barber returning to "The Ice Panel" after two series away. Phillip Schofield and Christine Bleakley returned to co-present. Head judge Robin Cousins and Barber were joined on "The Ice Panel" by former judge Jason Gardiner and former The Pussycat Dolls singer Ashley Roberts, who replaced Louie Spence and Katarina Witt.


title: Dancing on Ice

text: The ninth series of "Dancing on Ice" began airing on 5 January 2014. It was announced on 21 May 2013 by Christopher Dean and Jayne Torvill that it would be their last series as coaches, and ITV's Director of Television, Peter Fincham, confirmed that the programme would be cancelled after series 9. On 24 June 2013, it was reported that "Dancing on Ice" could continue with new coaches, however, on 22 October 2013 it was confirmed that this would be the show's last series.


title: Dancing on Ice

text: It was later announced that the ninth series would be an "all-star" series, featuring former winners and other contestants from the eight previous series. The 14-strong line up was revealed on 11 December 2013; it included six former champions, six other top-four finishers, plus Joe Pasquale and Todd Carty.


title: Dancing on Ice

text: Phillip Schofield and Christine Bleakley returned to co-present; Christopher Dean, Jayne Torvill and Karen Barber returned to mentor the celebrities; Robin Cousins, Jason Gardiner, Karen Barber and Ashley Roberts returned for their respective ninth, eighth, seventh and second series on "The Ice Panel". Cousins was absent for weeks 6 and 7 due to commentating the 2014 Winter Olympics, so former judge Nicky Slater returned in his place and Barber was temporary head judge.


title: Dancing on Ice

text: On 4 September 2017, it was announced on "This Morning" that "Dancing on Ice" would return with Willoughby and Schofield as presenters, and Torvill and Dean returning in new roles of head judges. It was also revealed that Jason Gardiner would be returning to the Ice Panel, along with Diversity member Ashley Banjo. With the announcement of the new series it was confirmed that the show would have a new set, new graphics, a new logo and a new theme tune, including the contestants and professionals faces for the first time. The show's new logo was released on the official Twitter account. The series will be filmed at RAF Bovingdon.


title: Dancing on Ice

text: It was announced on 25 January 2018 that "Dancing on Ice" would return for an eleventh series in 2019. The presenters and judges remain the same as for series 10, with the exception of Jordan Banjo, who was unable to return due to a clash of commitments. The participating celebrities began to be confirmed on 1 October 2018. This series is the first not to feature three-time "Dancing on Ice" champion Daniel Whiston, who instead took on the role of Associate Creative Director. Former judge Karen Barber also returned as head coach.


title: Dancing on Ice

text: In this series John Barrowman, a former contestant, joined as a judge, replacing Jason Gardiner. Jayne Torvill, Christopher Dean and Ashley Banjo also returned as judges. Series 12 began on 5 January 2020. On 18 December 2019, it was announced that Michael Barrymore, who was originally announced as a contestant, had withdrawn from the show due to a broken hand. He was later replaced by Radzi Chinyanganya.


title: Dancing on Ice

text: On 24 June 2020, it was announced that Alex Murphy, the show's reigning champion, had not been re-contracted for the upcoming series, and on 19 July 2020, that Brianne Delcourt would be leaving the show to spend more time with her husband, Kevin Kilbane, who she partnered last series. On 30 August 2020, it was announced that Alexander Demetriou and Carlotta Edwards wouldn't be on the main line-up of professional skaters. On 7 October 2020, it was announced that Jess Hatfield, Oscar Peter and Tom Naylor won't be returning either. They have all been replaced by returning professionals Andy Buchanan and Robin Johnstone and new professionals Angela Egan, Joe Johnson, Karina Manta, Klabera Komini and Yebin Mok.


title: Dancing on Ice

text: It was announced during the previous series final that the show would return for its fourteenth series. It was announced on 3 October 2021 that John Barrowman would not return to the judging panel. "Strictly Come Dancing" professional Oti Mabuse was later revealed as his replacement.


title: Dancing on Ice

text: It was announced during the final of the previous series that the show would return for its fifteenth series in January 2023. Professional skaters Andy Buchanan, Robin Johnstone, Angela Egan, Joe Johnson and reigning champion Karina Manta did not return for this series and were replaced by returning professionals Sylvain Longchambon, Vicky Ogden and Klabera Komini, as well as new professional skater Olivia Smart.


title: Dancing on Ice

text: Like many other reality TV shows, "Dancing on Ice" has had a number of supplementary shows. The first was "Dancing on Ice Defrosted". It was presented by Stephen Mulhern and aired on ITV2 immediately after the main ITV show and again after the results show. The show featured opinions from celebrity guests and past contestants as well as from Torvill and Dean, the judges, presenters and competitors. Judge Nicky Slater also offered in-depth analysis of various performances using the latest video technology that the judges use to judge performances.


title: Dancing on Ice

text: The second spin-off show was originally called "Dancing on Ice Extra" and was presented by Andi Peters and Andrea McLean, both competitors in the first series. Midway through the first series Paul O'Grady left ITV to join Channel 4 meaning that ITV had no show to put on air at 5 pm. The format of "Dancing on Ice Defrosted" was modified so that it could be broadcast every weekday. Due to Andrea's maternity leave during the second series she did not return to present the show and therefore Ben Shephard joined the show as the anchor presenter, and, unlike during the previous, series Andi Peters was now a roving reporter around the studio. For its second run the show was renamed "Dancing on Ice Exclusive". Neither of these first two spin-off shows returned in 2008 nor 2009.


title: Dancing on Ice

text: In 2010 it was announced that a new spin-off show would accompany "Dancing on Ice", named "Dancing on Ice Friday", presented by Ben Shephard and Coleen Nolan.


title: Dancing on Ice

text: This took place on Saturday 24 March 2007 and featured finalists from both Series 1 and Series 2. All six celebrities did one routine each, scored by the judges, and then voted on by the public. The two couples finishing first after the public voted skated again in the skate off to decide the winner. The skaters that did not reach the skate off – 3rd to 6th – were announced "in no particular order", so ranks may not be accurate.


title: Dancing on Ice

text: For Christmas 2008, Torvill and Dean went head to head with Jayne Torvill having a team of three female celebrities, and Christopher Dean having a team of three male celebrities. The judges were the usual line-up of Robin Cousins, Ruthie Henshall, Jason Gardiner, Karen Barber and Nicky Slater. Holly Willoughby and Phillip Schofield presented the 90-minute programme.


title: Dancing on Ice

text: Team Torvill scored 80 points to Team Dean's 79.5 and won the show by also receiving the majority of the audience votes.


title: Dancing on Ice

text: Suzanne Shaw received the perfect score of 30 for the third time in a row. In her last two appearances on the show she has picked up the trophy.


title: Dancing on Ice

text: A 30-minute prime time spin-off to "Dancing on Ice" premiered on 26 January 2008 and ran for a few episodes, presented solely by Holly Willoughby. This both showed some exclusive footage of the celebrities training for the Sunday night main show and followed Torvill and Dean on the search for a member of the public to perform on the "Dancing on Ice" final in 2009.


title: Dancing on Ice

text: This was shown after the announcement of the bottom two had been made but before the skate off. It showed Torvill and Dean's search for an entertainment act on ice, with auditions from all kinds of ice skaters. The winner skated live on the "Dancing on Ice 2009 final" and join Torvill and Dean on tour.


title: Dancing on Ice

text: From a shortlist of 20 acts, Torvill and Dean invited only four back to give another performance in the "Dancing on Ice" studio. The final four were:


title: Dancing on Ice

text: An Olympic special aired on 22 July 2012, before the London 2012 Summer Olympics. It featured medal-winning Olympic athletes.


title: Dancing on Ice

text: The one-off special featured the judges from series 7, with Phillip Schofield and Christine Bleakley returning as presenters. Torvill & Dean unveiled a new and specially-crafted performance. Head judge, Robin Cousins also performed a solo routine for first time in twelve years.


title: Dancing on Ice

text: The judges scores were added to the studio audiences votes to decide the winner. No public vote took place, as the programme was recorded earlier in the year.


title: Dancing on Ice

text: A brand new spin-off show for the 2010 series of "Dancing on Ice", appropriately called "Dancing on Ice Friday", gave viewers the insight to the training of the celebrities over the last week. It was presented by television presenter Ben Shephard and former contestant and "Loose Women" star Coleen Nolan. The show was broadcast from 8 pm to 8.30 pm on Friday evenings on ITV throughout the duration of the main shows season. STV who broadcast the main show did not broadcast this on the Friday evening but after repeating the previous week's main show on the following Saturday afternoon. Due to poor ratings, "Dancing on Ice Friday" was axed prior to the 2011 series.


title: Dancing on Ice

text: A Christmas special aired on 22 December 2019 featuring performances from all the couples of the series 12, previous winner Ray Quinn, series 11 contestant Gemma Collins, and Torvill and Dean. Jake Quickenden was also supposed to be performing, but on 13 November 2019, it was announced that he had to pull out due to a neck injury.


title: Dancing on Ice

text: Due to a number of early withdrawals and to give the remaining contestants sufficient time to recover from any injuries, series 13 was paused for one week and the episode scheduled to air on 21 February was replaced with a pre-recorded special celebrating the most memorable moments in the show's history.


title: Jean Genet

text: Jean Genet (; – ) was a French novelist, playwright, poet, essayist, and political activist. In his early life he was a vagabond and petty criminal, but he later became a writer and playwright. His major works include the novels "The Thief's Journal" and "Our Lady of the Flowers" and the plays "The Balcony", "The Maids" and "The Screens".


title: Jean Genet

text: Genet's mother was a prostitute who raised him for the first seven months of his life before placing him for adoption. Thereafter Genet was raised in the provincial town of Alligny-en-Morvan, in the Nièvre department of central France. His foster family was headed by a carpenter and, according to Edmund White's biography, was loving and attentive. While he received excellent grades in school, his childhood involved a series of attempts at running away and incidents of petty theft.


title: Jean Genet

text: After the death of his foster mother, Genet was placed with an elderly couple but remained with them less than two years. According to the wife, "he was going out nights and also seemed to be wearing makeup." On one occasion he squandered a considerable sum of money, which they had entrusted him for delivery elsewhere, on a visit to a local fair.


title: Jean Genet

text: For this and other misdemeanors, including repeated acts of vagrancy, he was sent at the age of 15 to Mettray Penal Colony where he was detained between 2 September 1926 and 1 March 1929. In "Miracle of the Rose" (1946), he gives an account of this period of detention, which ended at the age of 18 when he joined the Foreign Legion. He was eventually given a dishonorable discharge on grounds of indecency (having been caught engaged in a homosexual act) and spent a period as a vagabond, petty thief and prostitute across Europe—experiences he recounts in "The Thief's Journal" (1949).


title: Jean Genet

text: After returning to Paris in 1937, Genet was in and out of prison through a series of arrests for theft, use of false papers, vagabondage, lewd acts, and other offences. In prison, Genet wrote his first poem, "Le condamné à mort", which he had printed at his own cost, and the novel "Our Lady of the Flowers" (1944).


title: Jean Genet

text: In Paris, Genet sought out and introduced himself to Jean Cocteau, who was impressed by his writing. Cocteau used his contacts to get Genet's novel published, and in 1949, when Genet was threatened with a life sentence after ten convictions, Cocteau and other prominent figures, including Jean-Paul Sartre and Pablo Picasso, successfully petitioned the French President to have the sentence set aside. Genet would never return to prison.