OpenLLM-France/wikimedia huggingface dataset:
# Monotone class theorem

In measure theory and probability, the monotone class theorem connects monotone classes and 𝜎-algebras. The theorem says that the smallest monotone class containing an algebra of sets $G$ is precisely the smallest 𝜎-algebra containing $G.$ It is used as a type of transfinite induction to prove many other theorems, such as Fubini's theorem.

## Definition of a monotone class

A monotone class is a family (i.e. class) $M$ of sets that is closed under countable monotone unions and also under countable monotone intersections. Explicitly, this means $M$ has the following properties:
* if $A_{1},A_{2},\ldots \in M$ and $A_{1}\subseteq A_{2}\subseteq \cdots$ then ⋃$_{i=1}$$^∞$A$_i$∈M, {\textstyle {\textstyle \bigcup \limits _{i=1}^{\infty }}A_{i}\in M, } and
* if $B_{1},B_{2},\ldots \in M$ and $B_{1}\supseteq B_{2}\supseteq \cdots$ then ⋂$_{i=1}$$^∞$B$_i$∈M.{\textstyle {\textstyle \bigcap \limits _{i=1}^{\infty }}B_{i}\in M.}

## Monotone class theorem for sets

Monotone class theorem for sets — Let $G$ be an algebra of sets and define $M(G)$ to be the smallest monotone class containing $G.$ Then $M(G)$ is precisely the 𝜎-algebra generated by $G$; that is $\sigma (G)=M(G).$

## Monotone class theorem for functions

Monotone class theorem for functions — Let ${\mathcal {A}}$ be a π-system that contains $\Omega \,$ and let ${\mathcal {H}}$ be a collection of functions from $\Omega$ to $\mathbb {R}$ with the following properties:
* If $A\in {\mathcal {A}}$ then $\mathbf {1} _{A}\in {\mathcal {H}}$ where $\mathbf {1} _{A}$ denotes the indicator function of $A.$
* If $f,g\in {\mathcal {H}}$ and $c\in \mathbb {R}$ then $f+g$ and $cf\in {\mathcal {H}}.$
* If $f_{n}\in {\mathcal {H}}$ is a sequence of non-negative functions that increase to a bounded function $f$ then $f\in {\mathcal {H}}.$
Then ${\mathcal {H}}$ contains all bounded functions that are measurable with respect to $\sigma ({\mathcal {A}}),$ which is the 𝜎-algebra generated by ${\mathcal {A}}.$

### Proof

The following argument originates in Rick Durrett's Probability: Theory and Examples.
The assumption $\Omega \,\in {\mathcal {A}},$ (2), and (3) imply that ${\mathcal {G}}=\left\{A:\mathbf {1} _{A}\in {\mathcal {H}}\right\}$ is a 𝜆-system. By (1) and the π−𝜆 theorem, $\sigma ({\mathcal {A}})\subseteq {\mathcal {G}}.$ Statement (2) implies that ${\mathcal {H}}$ contains all simple functions, and then (3) implies that ${\mathcal {H}}$ contains all bounded functions measurable with respect to $\sigma ({\mathcal {A}}).$

## Results and applications

As a corollary, if $G$ is a ring of sets, then the smallest monotone class containing it coincides with the 𝜎-ring of $G.$
By invoking this theorem, one can use monotone classes to help verify that a certain collection of subsets is a 𝜎-algebra.
The monotone class theorem for functions can be a powerful tool that allows statements about particularly simple classes of functions to be generalized to arbitrary bounded and measurable functions.
# More Guitar Stories

More Guitar Stories is a studio album by guitarist Jim West. The album earned West a Grammy Award for Best New Age Album.
# Moomin (singer)

Moomin (むーみん) (born July 13, 1972) and styled as MOOMIN is a Japanese reggae artist. Along with a number of colleagues, he is responsible for the growth and popularity of Japan's reggae scene.
He is originally from Chigasaki, Kanagawa, and is married with two children. He works at Overheat Studios, and keeps his real name secret.
Moomin first appeared on the reggae scene in 1992, and traveled to Jamaica the following year. His official debut with a record label was in 1997 (under Ki/oon Records), and since 2003 he has been with Universal Music Group.

## Discography
### Singles

* Happy and Free (July 21, 1997)
* In the Rain (January 21, 1998)
* Feel Alright! (May 30, 1998)
* Kakegae no nai Mono (かけがえのないもの, Something with no Backup Copy) (January 21, 1999)
* Ride On (June 9, 1999)
* Big City (October 21, 1999)
* My Sweetest (November 20, 1999)
* Kimi wo Omou Yoru (キミを想う夜, The Night I Think of You) (November 15, 2000)
* Kanashimi ga Kieru made (悲しみが消えるまで, Until the Sadness is Extinguished) (February 28, 2001)
* @ the Dancehall featuring Corn Head (May 9, 2001)
* Summer Riddim 01 (August 8, 2001) (Moomin & Dōzan Miki)
* Straight Ahead (December 5, 2001)
* Kindan no Mori (禁断の森, Forbidden Forest) featuring Corn Head & Rude Boy Face (May 22, 2002)
* Natsu no Owari no Harmony (夏の終わりのハーモニー, Harmony of Summer's End) (July 24, 2002) Cover of Yōsui Inoue & Kōji Tamaki
* Itsumo Soba de (いつもそばで, Always There) (May 21, 2003)
* Saibai shitai ~ Sekai chū de~ (栽培したい～世界中で～, I Want to Help Things Grow Throughout the World) (August 6, 2003)
* Nebagiba (ネバギバ) (April 28, 2004)
* Joy of Life (March 30, 2005)
* Natsu Kirakira (夏キラキラ, Shining Summer) (May 25, 2005)
* Riverside Hotel (リバーサイド ホテル) (May 10, 2006) Cover of Yōsui Inoue

### Albums

* In My Life (July 1, 1998)
* Moments (July 28, 1999)
* Triple M (November 15, 2000) Remix Album
* Get Here (May 23, 2001)
* Natural High (July 24, 2002)
* Rise Again (June 25, 2003)
* The Best of Moomin (July 2, 2003)
* Rise Again Remixes (September 17, 2003)
* No More Trouble (June 23, 2004)
* Featuring Works (November 24, 2004)
* Link Up (June 22, 2005)
* Adapt (May 24, 2006) Cover Album

### DVD

* Moomin Live Tour 2004 "No More Trouble" (November 24, 2004)

### Other

* Shōnan no Kaze (湘南乃風)「Ōen Uta (応援歌) feat. Moomin」
* Dōzan Miki (三木道三)「Gekkō (月光) feat. Moomin」

## Radio

* Mother Music Records (JFN系) - PUSHIMと木曜23時より放送(2005年９月で終了)
# Montpellier folies

The folies of the French city of Montpellier are a number of châteaux on the outskirts of the city. Comparable to English country houses rather than follies in the usual sense of the term, they were built by the wealthy as summer residences from the 18th century onwards. Some of them had and still have their own vineyards and produce their own wines. Jean Giral and Charles Gabriel Leblanc were amongst the architects hired by the merchants.
The folies are the visible proof of the wealth of the region in the 18th century. Most of them are built in Renaissance style, with decorative gardens surrounding them. These gardens are in various styles, both French and Italianate as well as those designed in a 'natural' way, in a style resembling but pre-dating English garden style.
The folies are owned by wealthy families, and some of them still make wine (especially Flaugergues). Initially built as country houses outside the city, today they are mostly surrounded by suburbs, highways, outlet stores and the like. Below is a list of the chateaux:
* Château de Flaugergues 43°36′37.08″N 3°55′12.15″E﻿ / ﻿43.6103000°N 3.9200417°E﻿ / 43.6103000; 3.9200417﻿ (Château de Flaugergues)
* Château de la Mogère43°36′2″N 3°55′33″E﻿ / ﻿43.60056°N 3.92583°E﻿ / 43.60056; 3.92583﻿ (Château de la Mogère)
* Château d'O 43°38′00″N 3°50′21″E﻿ / ﻿43.63322222°N 3.839030556°E﻿ / 43.63322222; 3.839030556﻿ (Château d'O)
* Château de la Mosson 43°36′49″N 3°49′09″E﻿ / ﻿43.61372222°N 3.819119444°E﻿ / 43.61372222; 3.819119444﻿ (Château de la Mosson)
# Mordellistena griseolineata

Mordellistena griseolineata is a beetle in the genus Mordellistena of the family Mordellidae. It was described in 1937 by Maurice Pic.
# Bodybuilding at the 2006 Asian Games – Men's +90 kg

The men's +90 kilograms event at the 2006 Asian Games was held on December 9, 2006 at the Al-Dana Banquet Hall in Doha, Qatar.

## Schedule

All times are Arabia Standard Time (UTC+03:00)
| Date | Time | Event |
| Saturday, 9 December 2006 | 12:15 | Prejudging round |
| Saturday, 9 December 2006 | 18:05 | Final round |

## Results
### Prejudging round

| Rank | Athlete | Score |
| 1 | Tareq Al-Farsani (BRN) | 5 |
| 2 | Jassim Abdulla (QAT) | 11 |
| 3 | Ahmad Al-Saafeen (JOR) | 15 |
| 4 | Yang Sang-hun (KOR) | 19 |
| 5 | Mohamed Merza (BRN) | 22 |
| 6 | Fereydoun Haghi (IRI) | 30 |
| 7 | Mohsen Ghorannevis (IRI) | 36 |
| 8 | Hsu Chia-hao (TPE) | 39 |
| 9 | Fadi Zaazaa (LIB) | 46 |
| DQ | Mohammad Ullah (AFG) | 48 |
* Mohammad Ullah of Afghanistan originally got the 10th place, but was disqualified.

### Final round

| Rank | Athlete | Prej. | Final | Total |
| | Tareq Al-Farsani (BRN) | 5 | 5 | 10 |
| | Jassim Abdulla (QAT) | 11 | 12 | 23 |
| | Ahmad Al-Saafeen (JOR) | 15 | 13 | 28 |
| 4 | Yang Sang-hun (KOR) | 19 | 20 | 39 |
| 5 | Mohamed Merza (BRN) | 22 | 23 | 45 |
# Bodos Power Systems

Bodo's Power Systems, also known as Bodo's Power Systems Magazine, is a German monthly news magazine focusing exclusively on power electronics and is published in Laboe. The editor-in-chief is Bodo Arlt.

## Overview

Bodo's Power Systems was established in 2006. The magazine is part of A Media. It offers access to general power electronics information, industry news, and company specific solutions for power electronics applications. Articles are written as contributions by technology experts from the industry.

## Cost of usage

Bodo's Power Systems is financed by advertisements, and paper copies are distributed according to a free-of-charge subscription list.

## PowerGuru

In June 2012, the web-based power electronics information platform PowerGuru started a cooperation with Bodo's Power Systems and provides a fully searchable, categorizable, and commentable archive of all Bodo's Power Systems articles since its establishment in 2006.

## EE Power

In May 2016, Bodo's Power Systems partnered with EE Power, which is now the exclusive English language digital channel for the magazine's content.
# Bodotriidae

Bodotriidae is a family of crustaceans belonging to the order Cumacea. Bodotriids have a worldwide distribution in shallow and deep waters. There are over 380 described species in over 30 genera, being the most diverse cumacean family. Their external morphology differs from other cumaceans by a combination of traits that independently are not unique to the family: the telson is fused to the last abdominal segment (last pleonite), the dorsal part of the mandible has a boat shape (naviculoid), exopods exist on the third maxilliped and the first peraeopod, and there is a uropodal endopod with one or two articles.

## Anatomy

In both sexes the telson is fused with the last segment of the pleon, forming a "pleotelson". Males generally have five pairs of pleopods, although less often there may be three, two or they may be entirely absent. In females the second antenna is substantially shorter than the first. The third maxillipeds always have exopods (outer branches), and there are endopods (inner branches) on one or two segments of the uropods.

## Diversity

Bodotriidae is divided into three subfamilies (Bodotriinae, Mancocumatinae, and Vaunthompsoniinae), although it has been suggested that Mancocumatinae belong to the Vaunthompsoniinae:

### Bodotriinae Scott, 1901

* Alticuma Day, 1978
* Apocuma Jones, 1973
* Atlantocuma Bacescu & Muradian, 1974
* Austrocuma Day, 1978
* Bacescuma Petrescu, 1998
* Bodotria Goodsir, 1843
* Cyclaspis Sars, 1865
* Cyclaspoides Bonnier, 1896
* Eocuma Marcusen, 1894
* Iphinoe Bate, 1856
* Mossambicuma Day, 1978
* Pseudocyclaspis Edwards, 1984
* Stephanomma Sars, 1871
* Upselaspis Jones, 1955
* Zygosiphon Calman, 1907

### Mancocumatinae Watling, 1977

* Mancocuma Zimmer, 1943
* Pseudoleptocuma Watling, 1977
* Speleocuma
* Spilocuma Watling, 1977

### Vaunthompsoniinae

* Bathycuma Hansen, 1895
* Cumopsis G. O. Sars, 1865
* Gaussicuma Zimmer, 1907
* Gephyrocuma Hale, 1936
* Gigacuma Kurian, 1951
* Glyphocuma Hale, 1944
* Heterocuma Miers, 1879
* Hypocuma Jones, 1973
* Leptocuma Sars, 1873
* Paravaunthompsonia Mühlenhardt-Siegel, 2008
* Picrocuma Hale, 1936
* Pomacuma Hale, 1944
* Pseudosympodomma Kurian, 1954
* Scyllarocuma
* Sympodomma Stebbing, 1912
* Vaunthompsonia Bate, 1858
* Zenocuma Hale, 1944
# Moroxydine

Moroxydine is an antiviral drug that was originally developed in the 1950s as an influenza treatment. It has potential applications against a number of RNA and DNA viruses. Structurally moroxydine is a heterocyclic biguanidine.
It was reported in March 2014 that three kindergartens in two provinces of China had been found to be secretly dosing their students with moroxydine hydrochloride to try to prevent them from becoming ill. The kindergartens are paid only for the days that pupils attend and wanted to ensure that they maximised their earnings.
# Bofors 25 mm M/32

The Bofors 25 mm M/32 was a Swedish- designed and built light anti-aircraft gun that was used aboard ships of the Swedish Navy during the Second World War.

## History

The development of Bofors first automatic weapons began in 1925 when the Navy requested the development of a 20 mm anti-aircraft gun. In 1928 the Navy requested a new 40 mm AA gun and a 25 mm AA gun which was produced in parallel and known as the M/32.

## Design

The M/32 was designed with a barrel 64 calibers in length, fired a 25×205mmR cartridge, at 160–180 rpm and with a muzzle velocity of 850 m/s. Later a shorter version firing a 25×187mmR cartridge was produced in limited numbers. The M/32 looked similar to its larger 40 mm sibling and used the same long-recoil operating system and hydro-spring recoil mechanism. Its feed mechanism consisted of 6-round clips which were held in a vertical frame above the gun breech. Two clips were mounted side by side so that continuous fire could be maintained without the need to pause and change magazines. The clips were in two halves, which split and fell away as the cartridges entered the frames.
The gun was available in fixed single mount, fixed twin mount or on a mobile four-wheeled carriage with twin collapsible outriggers. In addition to fixed pedestal mounts, a retractable gun mount was designed for submarine use. Although available in land mounts it was primarily a naval weapon. At first the 40 mm gun was considered to be too heavy, so preference was given to single and twin mounts of the M/32 aboard ships of the Swedish navy.

## Gallery

* A single M/32 mount aboard HSwMS Malmö
* A single M/32 mount at Vaxholm Fortress, Sweden.
* A twin M/32 at Vaxholm Fortress, Sweden.
* A twin M/32 at Vaxholm Fortress, Sweden.
# Boharina

Boharina (pronounced) is a settlement in the Municipality of Zreče in northeastern Slovenia. It lies in the foothills of the Pohorje Hills, above the left bank of the upper Dravinja River, just north of Zreče. The area is part of the traditional region of Styria. It is now included with the rest of the municipality in the Savinja Statistical Region.
# Morning Star (comics)

Morning Star is the alias of Schuyler Belial, a fictional villain appearing in American comic books published by Marvel Comics. The character has been depicted as an enemy of Moon Knight and the Werewolf by Night. He first appeared in Moon Knight #29. He was created by Doug Moench and Bill Sienkiewicz.

## Fictional character biography

Morning Star was the leader of a group of Satanists known as the Followers of the Left Hand Path. He and his cult spent a year tracking Jack Russell, the increasingly feral Werewolf by Night, the blood of whom Belial thought could be used to "reinvigorate" his followers by turning them into werewolves. In Los Angeles, the cult captured the werewolf, who escaped shortly thereafter, but not before the cult had implanted a tracking device in the creature's skull.
The Werewolf by Night fled to New York City, where the superhero Moon Knight attempted to aid him. They were both later captured by Morning Star and his cult, and taken to Morning Star's offices in the penthouse of New York City's Tishman Building, at 666 Fifth Avenue.
Morning Star planned to use Moon Knight as a human sacrifice, and afterwards to have his followers drink the blood of the Werewolf by Night to give them "the power of the Beast". However, Moon Knight escaped his captors and helped the Werewolf by Night escape as well. Morning Star immediately sent his men to recapture the two, but the cultists were defeated. Moon Knight and the Werewolf by Night later infiltrated the cult, returning to Morning Star's offices, where they engaged in battle to defeat the rest of the members. During this melee, the Werewolf by Night threw Morning Star from the roof of the 41-story Tishman Building, killing him.
# Moongan, Queensland

Moongan is a rural locality in the Rockhampton Region, Queensland, Australia. In the 2021 census, Moongan had a population of 120 people.

## History

The locality takes its name from the former Moongan railway station (23°36′23″S 150°23′49″E﻿ / ﻿23.6064°S 150.3969°E﻿ / -23.6064; 150.3969﻿ (Moongan railway station)) on the former Dawson Valley railway line. It is believed to be an Aboriginal word meaning top of hill.
The section of the railway line from Moonmera railway station to Mount Morgan opened on 26 November 1898. The section between Moonmera and Moongan involves a steep climb up the Razorback Range with a gradient too steep for a steam locomotive, so an Abt rack engine was additionally used on this section.

## Demographics

In the 2016 census, Moongan had a population of 118 people.
In the 2021 census, Moongan had a population of 120 people.

## Education

There are no schools in Moongan. The nearest government primary and secondary schools are Mount Morgan State School and Mount Morgan State High School, both in Mount Morgan to the south.
# Moongardie Community

Moongardie is a small Aboriginal community, located 110 kilometres (68 mi) east of Halls Creek in the Kimberley region of Western Australia, within the Shire of Halls Creek.

## Native title

The community is located within the registered Gooniyandi Combined 2 (WAD6008/00) native title claim area.

## Education

Children of school age at Moongardie attend the Yiyili Community School. The school caters for students in kindergarten to Year 10 from Yiyili and the surrounding outstations of Ganinyi, Girriyoowa, Goolgaradah, Kurinyjarn, and Rocky Springs. In 2010 there were 72 students enrolled. A daily bus service operated by the school collects students from other nearby communities including Moongardie 30 kilometres (19 mi) distant. The school provides lunch for students. Students who progress beyond Year 10 attend boarding school in Darwin, Northern Territory, and other larger towns.

## Governance

The community is managed through its incorporated body, Moongardie Indigenous Corporation (formerly Moongardie Aboriginal Corporation), incorporated under the Aboriginal Councils and Associations Act 1976 on 11 February 1992.

## Moongardie

Moongardie Layout Plan No.1 was prepared in accordance with State Planning Policy 3.2 Aboriginal Settlements, and was endorsed by the community in 1999 and the Western Australian Planning Commission in 2001. The layout plan map-set and background report can be viewed at Planning Western Australia.
# Morum fatimae

Morum fatimae is a species of sea snail, a marine gastropod mollusk in the family Harpidae, the harp snails.

## Distribution

It is found in the Mozambique Channel.
# Moraviensis

Moraviensis may refer to:
* Enterococcus moraviensis, species of bacteria
* Pseudomonas moraviensis, species of bacteria
# Morán Morán

Morán Morán is a contemporary art gallery in Los Angeles. It was founded by Al Moran in 2008 as OHWOW, and was later renamed. The gallery began as an alliance of artists and curators presenting various exhibitions and publications. It is located at 641 N. Western Avenue, Los Angeles, CA 90004.

## History

As of spring 2011, Morán Morán opened a gallery location in Los Angeles, designed by New York City architect Rafael de Cárdenas. In 2021, the gallery opened a second gallery space located in the Polanco, Mexico City.
Former partner Aaron Bondaroff resigned from the gallery in February 2018 after multiple accusations of inappropriate sexual behavior towards women. The gallery's name was changed from Morán Bondaroff to Morán Morán.
# Boophis williamsi

Boophis williamsi is a species of frog in the family Mantellidae endemic to Madagascar. Its natural habitats are subtropical or tropical moist montane forests, subtropical or tropical high-altitude grassland, rivers, and heavily degraded former forests. It is threatened by habitat loss.
# Boopi River

The Boopi River is a river of Bolivia.
# Moseć

Moseć is a village in Šibenik-Knin County, Croatia. The settlement is administered as a part of Ružić municipality. In the 2011 census, it had a total of 75 inhabitants.
# Bonham Strand (tailor)

Bonham Strand is a brand of bespoke tailored suits based in Hong Kong.

## History

Bonham Strand was founded in Hong Kong in April 2012. It was named Bonham Strand as the company headquarters are located in Bonham Strand, Sheung Wan in Hong Kong.

## Overview

Bonham Strand has a partnership with established Italian fabrics provider Cerruti. The company emphasizes that all suits are made in Hong Kong. The tailors are local and the company has a social aspect by hiring rehabilitated drug addicts to become apprentices.
Besides reaching out to corporate sponsors, Bonham Strand is the first tailor to reach out to the Hong Kong Government for support to help revive the tailoring industry in Hong Kong as well as helping with unemployed youths.
# Bondei language

Bondei is a Northeast Coast Bantu of Tanzania closely related to Shambala.
# Bonpas Township, Richland County, Illinois

Bonpas Township is located in Richland County, Illinois. As of the 2010 census, its population was 390 and it contained 160 housing units.

## History

Bonpas Township was formed after an 1858 election, in which county voters chose to adopt a township-based model of county government, in place of the old precinct-based system.$^{:622}$ Named for Bonpas Creek, which flows through its boundaries, the township was originally heavily wooded. Early settlers favored this part of Richland County above others, but as experience taught the value of flat prairie ahead of hilly woodlands, the township languished. Before the coming of the Ohio and Mississippi Railway, when good transportation was unavailable, most coal and stone used in Richland County came from Bonpas Township.$^{:626}$

## Geography

According to the 2010 census, the township has a total area of 37.53 square miles (97.2 km$^2$), of which 37.53 square miles (97.2 km$^2$) (or 100%) is land and 0.01 square miles (0.026 km$^2$) (or 0.03%) is water.
# Bombay and Moira Railroad

The Bombay and Moira Railroad is a historic railroad in New York.
The Saratoga and St. Lawrence Railroad began operations on December 27, 1888 on a line running from Moira to Bombay. The S&SL was reincorporated on March 31, 1898 as the Bombay and Moira Railroad.
The B&M was abandoned in 1900 after being purchased by the Grand Trunk Railway and torn up for scrap.
The right-of-way is still visible due to lack of property development and encroaching vegetation.
# Moses Maverick

Moses Maverick (1611—1686) was a 17th-century English colonist who migrated to the Massachusetts Bay Colony and founded Marblehead, Massachusetts. He served as selectman for 14 years. Maverick Street, Maverick Cove, Maverick Court and Moses Maverick Square are named after him.

## Biography

Moses Maverick was born in Devon, England to Rev. John Maverick and Mary Gye. Moses Maverick's older brother is early Massachusetts colonist Samuel Maverick.
Maverick migrated to Dorchester, Massachusetts with his father, soon to become the first minister in Dorchester, in 1630. He became a freeman in 1634. Eventually, Maverick left Dorchester for Salem, settling in the outskirts of town in what was soon to become Marblehead. Through his efforts, Marblehead became a separate entity from Salem in 1649. In reward for these efforts, he was elected as one of the first selectmen in 1649, a position he would hold for fourteen years between 1649 and his death. He held various other local positions and was the town's leading figure.
Moses Maverick died in Marblehead in 1686 at the age of 74.

## Personal life

Moses Maverick married twice. First, to Remember Allerton, daughter to Isaac Allerton, who had come over on the Mayflower. His second wife was Eunice Cole and they were married by Governor John Endecott.
# Motion tracker

Motion tracker can refer to:
* Motion detector, a device that utilizes a sensor to detect nearby motion
* Motion capture, the process of recording the movement of objects or people