query: What does a theodolite measure?

title: Theodolite

text: does not measure vertical angles, and is used only for levelling on a horizontal plane. Temporary adjustments are a set of operations necessary in order to make a theodolite ready for taking observations at a station. These include its setting up, centering, leveling up and elimination of parallax, and are achieved in four steps: Sightings are taken by the surveyor, who adjusts the telescope's vertical and horizontal angular orientation so the cross-hairs align with the desired sighting point. Both angles are read either from exposed or internal scales and recorded. The next object is then sighted and recorded without moving

title: Theodolite

text: These angles can be measured with great accuracy, typically to milliradian or seconds of arc. From these readings a plan can be drawn, or objects can be positioned in accordance with an existing plan. The modern theodolite has evolved into what is known as a total station where angles and distances are measured electronically, and are read directly to computer memory. In a transit theodolite, the telescope is short enough to rotate through the zenith, otherwise for non-transit instruments vertical (or altitude), rotation is restricted to a limited arc. The optical level is sometimes mistaken for a theodolite, but it

title: Theodolite

text: later became associated with the altazimuth instrument. The 1728 "Cyclopaedia" compares "graphometer" to "half-theodolite". Even as late as the 19th century, the instrument for measuring horizontal angles only was called a "simple theodolite" and the altazimuth instrument, the "plain theodolite". The first instrument more like a true theodolite was likely the one built by Joshua Habermel (Erasmus Habermehl) in Germany in 1576, complete with compass and tripod. The earliest altazimuth instruments consisted of a base graduated with a full circle at the limb and a vertical angle measuring device, most often a semicircle. An alidade on the base was used

title: Theodolite

text: Theodolite A theodolite is a precision optical instrument for measuring angles between designated visible points in the horizontal and vertical planes. The traditional use has been for land surveying, but they are also used extensively for building and infrastructure construction, and some specialized applications such as meteorology and rocket launching. It consists of a moveable telescope mounted so it can rotate around horizontal and vertical axes and provide angular readouts. These indicate the orientation of the telescope, and are used to relate the first point sighted through the telescope to subsequent sightings of other points from the same theodolite position.

title: Theodolite

text: to sight an object for horizontal angle measurement, and a second alidade was mounted on the vertical semicircle. Later instruments had a single alidade on the vertical semicircle and the entire semicircle was mounted so as to be used to indicate horizontal angles directly. Eventually, the simple, open-sight alidade was replaced with a sighting telescope. This was first done by Jonathan Sisson in 1725. The theodolite became a modern, accurate instrument in 1787, with the introduction of Jesse Ramsden's famous great theodolite, which he created using a very accurate dividing engine of his own design. The demand could not be

title: Theodolite

text: of theodolite use in measuring winds aloft, by using specially-manufactured theodolites to track the horizontal and vertical angles of special weather balloons called "ceiling balloons" or "pilot balloons" ("pibal"). Early attempts at this were made in the opening years of the nineteenth century, but the instruments and procedures weren't fully developed until a hundred years later. This method was extensively used in World War II and thereafter, and was gradually replaced by radio and GPS measuring systems from the 1980s onward. The pibal theodolite uses a prism to bend the optical path by 90 degrees so the operator's eye position

title: Theodolite

text: and "λιτός" "plain". It has been also suggested that "-delitus" is a variation of the Latin supine "deletus", in the sense of "crossed out". There is some confusion about the instrument to which the name was originally applied. Some identify the early theodolite as an azimuth instrument only, while others specify it as an altazimuth instrument. In Digges's book, the name "theodolite" described an instrument for measuring horizontal angles only. He also described an instrument that measured both altitude and azimuth, which he called a "topographicall instrument" . Thus the name originally applied only to the azimuth instrument and only

title: Theodolite

text: 180 degrees about the vertical axis, the instrument can be used in 'plate-left' or 'plate-right' modes ('plate' refers to the vertical protractor circle). By measuring the same horizontal and vertical angles in these two modes and then averaging the results, centering and collimating errors in the instrument can be eliminated. Some transit instruments are capable of reading angles directly to thirty arc-seconds (≈ 0.15 mrad). Modern theodolites are usually of the transit-theodolite design, but engraved plates have been replaced with glass plates designed to be read with light-emitting diodes and computer circuitry, greatly improving accuracy. There is a long history

title: Complete measure

text: Naïvely, we would take the "σ"-algebra on R to be "B" ⊗ "B", the smallest "σ"-algebra containing all measurable "rectangles" "A" × "A" for "A" ∈ "B". While this approach does define a measure space, it has a flaw. Since every singleton set has one-dimensional Lebesgue measure zero, for "any" subset "A" of R. However, suppose that "A" is a non-measurable subset of the real line, such as the Vitali set. Then the "λ"-measure of {0} × "A" is not defined, but and this larger set does have "λ"-measure zero. So, this "two-dimensional Lebesgue measure" as just defined is not

title: Tree height measurement

text: is measured. The vertical distance added by the pole to the tape length is (sin Θ x pole length). There are several additional methods that can be used to measure tree heights from a distance that can produce reasonably accurate results. These include traditional surveying methods using a theodolite, cross-triangulation, the extended baseline method, the parallax method, and the triangle method. Standard surveying techniques may be used to measure tree heights. A theodolite with an electronic distance measurement (EDM0 function or Total Station can provide accurate heights because a specific point on the tree crown could be consistently chosen and

title: Theodolite

text: does not change as the elevation is changed through a complete 180 degrees. The theodolite is typically mounted on a rugged steel stand, set up so it is level and pointed north, with the altitude and azimuth scales reading zero degrees. A balloon is released in front of the theodolite, and its position is precisely tracked, usually once a minute. The balloons are carefully constructed and filled, so their rate of ascent can be known fairly accurately in advance. Mathematical calculations on time, rate of ascent, azimuth and angular altitude can produce good estimates of wind speed and direction at

title: Theodolite

text: positioning use a similar mounting system. The height of the reference point of the theodolite—or the target—above the ground benchmark must be measured precisely. The term transit theodolite, or transit for short, refers to a type of theodolite that was developed in the early 19th century. It was popular with American railroad engineers pushing west, and it replaced the railroad compass, sextant and octant. It features a vertical circle which is graduated through the full 360 degrees and a telescope that could "flip over" ("transit the scope"). By reversing the telescope and at the same time rotating the instrument through

title: Theodolite

text: Collimation error - The optical axis of the telescope, must also be perpendicular to the horizontal axis. If not, then a "collimation error" exists. Index error, horizontal-axis error ('trunnion-axis error') and collimation error are regularly determined by calibration and are removed by mechanical adjustment. Their existence is taken into account in the choice of measurement procedure in order to eliminate their effect on the measurement results of the theodolite. The term "diopter" was sometimes used in old texts as a synonym for theodolite. This derives from an older astronomical instrument called a dioptra. Prior to the theodolite, instruments such as

title: Theodolite

text: cannot be used at the poles where the Earth's axis is precisely perpendicular to the horizontal axis of the spinner, indeed it is not normally used within about 15 degrees of the pole because the east-west component of the Earth's rotation is insufficient to obtain reliable results. When available, astronomical star sights are able to give the meridian bearing to better than one hundred times the accuracy of the gyrotheodolite. Where this extra precision is not required, the gyrotheodolite is able to produce a result quickly without the need for night observations. Theodolite A theodolite is a precision optical instrument

title: Theodolite

text: Yorkshireman from Halifax, England who had developed the dividing engine for dividing angular scales accurately to within a second of arc (≈ 0.0048 mrad or 4.8 µrad), was commissioned to build a new instrument for the British Ordnance Survey. The Ramsden theodolite was used over the next few years to map the whole of southern Britain by triangulation. In network measurement, the use of forced centering speeds up operations while maintaining the highest precision. The theodolite or the target can be rapidly removed from, or socketed into, the forced centering plate with sub-millimeter precision. Nowadays GPS antennas used for geodetic

title: Theodolite

text: interesting waterborne version of the theodolite (using a pendulum device to counteract wave movement) was invented by Edward Samuel Ritchie. It was used by the U.S. Navy to take the first precision surveys of American harbors on the Atlantic and Gulf coasts. In the early part of the 20th century, Heinrich Wild produced theodolites that became popular with surveyors. His Wild T2, T3, and A1 instruments were made for many years, and he would go on to develop the DK1, DKM1, DM2, DKM2, and DKM3 for Kern Aarau company. With continuing refinements, instruments steadily evolved into the modern theodolite used

title: What Kate Does

text: week." VanDerWerff of the "LA Times", Ryan of the "Chicago Tribune", Sepinwall of "The Star-Ledger", Jensen of "Entertainment Weekly" and Mark Medley of the "National Post" also found the episode to contain humorous lines. This episode was watched by 11 million American viewers and 1.57 million Canadian viewers. What Kate Does "What Kate Does" is the 106th television episode of the American Broadcasting Company's "Lost" and third episode of the sixth season. It was written by executive producers Edward Kitsis and Adam Horowitz and directed in September 2009 by Paul Edwards. "What Kate Does" was first aired February 9, 2010,

title: What Kate Does

text: What Kate Does "What Kate Does" is the 106th television episode of the American Broadcasting Company's "Lost" and third episode of the sixth season. It was written by executive producers Edward Kitsis and Adam Horowitz and directed in September 2009 by Paul Edwards. "What Kate Does" was first aired February 9, 2010, on ABC in the United States and on CTV in Canada. Kate Austen is the character on whom the episode is centered. In December 2007, Kate Austen chases after James "Sawyer" Ford (Josh Holloway), who escapes from the Others' captivity in the island's temple and is grieving over

title: What She Does Best

text: What She Does Best What She Does Best is a studio album by country singer Lynn Anderson, released in 1988. It was her only album with Mercury records. Notable due to featuring her last charting single, "What She Does Best" did not chart and was commercially unsuccessful. It would be her last album for four years, as Anderson went into a brief retirement and officially retired from releasing singles. The singles from this disc were "Under the Boardwalk" (a cover version of The Drifters' hit), "What He Does Best", and "How Many Hearts". "Under the Boardwalk" reached No. 24; the

title: What Kate Does

text: reviews"; however, this was down significantly from the previous episode's 89 and Bonnie Covel of About.com noted that " 'What Kate Does' brought us a bit of negativity. In general, fans just didn't like the episode". "What Kate Does" was largely considered to be a step down from the season premiere in pacing, revelations and writing; Mike Hale of "The New York Times" described the episode as "contemplative", "anticlimactic" and "subdued" and the flash sideways as "kind of boring and seemingly pointless." Chris Carabott of IGN, who gave the episode a score of 7.3 summed up that " 'What Kate

title: What She Does Best

text: other singles charted far outside the Top 40. "How Many Hearts" was the last single Anderson released, and it peaked at No. 69 on the country charts in 1989. The album's cover shows Anderson leaning on a fancy sports car, wearing a classic 1980s outfit. What She Does Best What She Does Best is a studio album by country singer Lynn Anderson, released in 1988. It was her only album with Mercury records. Notable due to featuring her last charting single, "What She Does Best" did not chart and was commercially unsuccessful. It would be her last album for four

title: The purpose of a system is what it does

text: be balanced by a more straightforwardly descriptive view. The term is used in many fields including biology and management. The purpose of a system is what it does The purpose of a system is what it does (POSIWID) is a systems thinking heuristic coined by Stafford Beer. Stafford Beer coined the term POSIWID and used it many times in public addresses. In his address to the University of Valladolid, Spain, in October 2001, he said "According to the cybernetician, the purpose of a system is what it does. This is a basic dictum. It stands for bald fact, which makes

title: The purpose of a system is what it does

text: The purpose of a system is what it does The purpose of a system is what it does (POSIWID) is a systems thinking heuristic coined by Stafford Beer. Stafford Beer coined the term POSIWID and used it many times in public addresses. In his address to the University of Valladolid, Spain, in October 2001, he said "According to the cybernetician, the purpose of a system is what it does. This is a basic dictum. It stands for bald fact, which makes a better starting point in seeking understanding than the familiar attributions of good intention, prejudices about expectations, moral judgment,

title: P.S.K. What Does It Mean?

text: was first used on the song "Rock 'N' Roll" which later became "You'll Be Under My Wheels". The second time they used it is from a song called "Lyrical Terrorist" which later became "Serial Thrilla", but it was soon used on the album "The Day Is My Enemy". P.S.K. What Does It Mean? "P.S.K. What Does It Mean?" (also written as "P.S.K. (What Does It Mean?)") is a song released in 1985 by Philadelphia rapper Schoolly D on his independent label Schoolly D Records. P.S.K. is the abbreviation for Park Side Killas, a street gang with which Schoolly D was

title: P.S.K. What Does It Mean?

text: P.S.K. What Does It Mean? "P.S.K. What Does It Mean?" (also written as "P.S.K. (What Does It Mean?)") is a song released in 1985 by Philadelphia rapper Schoolly D on his independent label Schoolly D Records. P.S.K. is the abbreviation for Park Side Killas, a street gang with which Schoolly D was affiliated. The highly influential song is considered the first hardcore rap song and features incidents of graphic sex, gunplay, drug references and one of the first uses of the word "nigga" in a rap song (earlier uses include "Scoopy Rap" and "Family Rap" in 1979, and "New York

title: What Difference Does It Make?

text: What Difference Does It Make? "What Difference Does It Make?" is a song by the English rock band the Smiths, written by singer Morrissey and guitarist Johnny Marr. It was the band's third single and is featured on their debut album, "The Smiths". A different version, recorded for the John Peel Show on BBC Radio 1, is included in the compilation album "Hatful of Hollow". The song was one of the band's first significant chart hits, peaking at No. 12 in the UK Singles Chart. However, Morrissey has said "What Difference Does It Make?" is among his least favourite songs

title: What Difference Does It Make?

text: and the covers featuring Morrissey are now very rare and collectible. "What Difference Does It Make?" was released without an accompanying music video. Speaking to Tony Fletcher on "The Tube" in 1984, Morrissey remarked that he felt that the video market was something that was going to "die very quickly", and that he wanted to "herald the death" of it. What Difference Does It Make? "What Difference Does It Make?" is a song by the English rock band the Smiths, written by singer Morrissey and guitarist Johnny Marr. It was the band's third single and is featured on their debut

title: Theodolite

text: error". This can only be checked on transit instruments. Horizontal axis error - The horizontal and vertical axes of a theodolite must be perpendicular; if not then a "horizontal axis error" exists. This can be tested by aligning the tubular spirit bubble parallel to a line between two footscrews and setting the bubble central. A horizontal axis error is present if the bubble runs off central when the tubular spirit bubble is reversed (turned through 180°). To adjust, the operator removes 1/2 the amount the bubble has run off using the adjusting screw, then re-level, test and refine the adjustment.

title: Theodolite

text: normal theodolite with an attachment that contains a gyroscope mounted so as to sense rotation of the Earth and from that the alignment of the meridian. The meridian is the plane that contains both the axis of the Earth's rotation and the observer. The intersection of the meridian plane with the horizontal contains the true north-south geographic reference bearing required. The gyrotheodolite is usually referred to as being able to determine or find true north. A gyrotheodolite will function at the equator and in both the northern and southern hemispheres. The meridian is undefined at the geographic poles. A gyrotheodolite

title: Theodolite

text: met by foreign theodolites owing to their inadequate precision, hence all instruments meeting high precision requirements were made in England. Despite the many German instrument builders at the turn of the century, there were no usable German theodolites available. A transition was brought about by Breithaupt and the symbiosis of Utzschneider, Reichenbach and Fraunhofer. As technology progressed, in the 1840s, the vertical partial circle was replaced with a full circle, and both vertical and horizontal circles were finely graduated. This was the "transit theodolite". Theodolites were later adapted to a wider variety of mountings and uses. In the 1870s, an

title: Theodolite

text: of the word "theodolite" is found in the surveying textbook "A geometric practice named Pantometria" (1571) by Leonard Digges, which was published posthumously by his son, Thomas Digges. The etymology of the word is unknown. The first part of the New Latin "theo-delitus" might stem from the Greek "θεᾶσθαι", "to behold or look attentively upon" or "θεῖν" "to run", but the second part is more puzzling and is often attributed to an unscholarly variation of one of the following Greek words: "δῆλος", meaning "evident" or "clear", or "δολιχός" "long", or "δοῦλος" "slave", or an unattested Neolatin compound combining "ὁδός" "way"

title: What Does Anything Mean? Basically

text: of its icy church keyboards and delay-ridden guitars". Chris Jenkins, in the book "The Rough Guide to Rock", however, called it "as half-baked as its title". What Does Anything Mean? Basically What Does Anything Mean? Basically is the second studio album by English post-punk band the Chameleons. It was recorded in January 1985 and released 1 October 1985 by record label Statik. One single was released from the album: "Singing Rule Britannia (While the Walls Close In)". "What Does Anything Mean? Basically" was recorded in January 1985 at Highland Studios in Inverness, Scotland. The album's sole single, "Singing Rule Britannia

title: What Does Anything Mean? Basically

text: What Does Anything Mean? Basically What Does Anything Mean? Basically is the second studio album by English post-punk band the Chameleons. It was recorded in January 1985 and released 1 October 1985 by record label Statik. One single was released from the album: "Singing Rule Britannia (While the Walls Close In)". "What Does Anything Mean? Basically" was recorded in January 1985 at Highland Studios in Inverness, Scotland. The album's sole single, "Singing Rule Britannia (While the Walls Close In)", was released on 1 August 1985. This song used uncredited Lennon-McCartney lyrics, with the final passage of the song quoting key

title: What Kate Does

text: the death of his love Juliet Burke (Elizabeth Mitchell) just hours earlier. In flash sideways to September 22, 2004, Kate assists a pregnant Claire Littleton (Emilie de Ravin) while on the run as a fugitive. The title alludes to the second season episode "What Kate Did". "What Kate Does" was watched by eleven million Americans and received mixed reviews by audiences and critics alike. In flash sideways, Kate Austen (Evangeline Lilly) flees LAX in a taxicab she has hijacked, in which a pregnant Claire Littleton (Emilie de Ravin) is a passenger. The cab driver (David H. Lawrence XVII) bails and

title: What Does It Take (To Keep a Man Like You Satisfied)

text: What Does It Take (To Keep a Man Like You Satisfied) "What Does It Take (To Keep a Man Like You Satisfied)" is a song written by Jim Glaser, that was recorded and released as a single in 1967 by American country artist, Skeeter Davis. Jim Glaser was a member of the popular country music group, Tompall and the Glaser Brothers. "What Does It Take (To Keep a Man Like You Satisfied)" was recorded at the RCA Victor Studio in Nashville, Tennessee, United States on May 1, 1967, one month before it was released. The session was produced by Felton

text: Jarvis. The song was released as a single officially in June 1967. "What Does It Take (To Keep a Man Like You Satisfied)" reached a peak of number five on the "Billboard Magazine" Hot Country Singles chart later that year. The single became Davis' first top-ten country hit in three years since 1964's "Gonna Get Along Without You Now" reached number eight. Additionally, "What Does It Take" was Davis' first entry onto the "Billboard" Bubbling Under Hot 100 since 1965, reaching a peak of twenty-one. The song was eventually released onto a studio album of the same name. What Does

title: What Does the K Stand For?

text: What Does the K Stand For? What Does the K Stand For? is a BBC Radio Four sitcom series based on the experiences of comedian Stephen K. Amos growing up as a teenager in south London in the 1980s. The broadcast of the first series began in November 2013; the third series commenced in January 2017. Reviewing Series 1, Episode 1 for "Radio Times", Tristram Fane Saunders found the show suited Amos "down to the ground; there's a touch of "Seinfeld" about "What Does the K Stand for?" in the way it flows from stand up into a deliciously awkward

title: What Does the Bee Do?

text: the bomb that Slater set explodes, badly burning one of them. "What Does The Bee Do?" is a children's poem from the late 1800s by Christina Rossetti. Margaret Schroeder's daughter recites it in the episode. "IGN" gave the episode a score of 8.5 out of 10, saying that it "effortlessly hits that sweet spot between advancing the plot while developing characters, much in the same way that the Season 2 premiere did." "The A.V. Club" rated the episode an "A-". The episode was watched by 2.546 million viewers. It fell two tenths, to 1.0 million adults 18-49 rating. What Does

title: The Measure of a Man: A Spiritual Autobiography

text: his upbringing and the invaluable legacy of his parents. Just a few years after his introduction to indoor plumbing and the automobile, Poitier broke racial barrier after racial barrier to launch a pioneering acting career. Committed to the notion that what one does for a living shows who one is, Poitier chose to play forceful and affecting characters who said something positive, useful, and lasting about the human condition. "The true measure of a man is in how he provided for his children" this was one lesson Sidney learnt from his father and held dear to his heart all his

title: What Does Anything Mean? Basically

text: lyrics of the Beatles song "She Said, She Said". "What Does Anything Mean? Basically" was released 1 October 1985 on record label Statik. "What Does Anything Mean? Basically" has been generally well received by critics. In his retrospective review, Ned Raggett of AllMusic called it "[a] rarity of sophomore albums, something that at once made the band all the more unique in its sound while avoiding a repetition of earlier work. [...] an astounding record." "Trouser Press" called it "even better" than "Script of the Bridge", "with much stronger production underscoring both the band's direct power and the ghostly atmospherics

title: What Does the Bee Do?

text: What Does the Bee Do? "What Does the Bee Do?" is the fourth episode of the second season of the HBO television series "Boardwalk Empire", and 16th episode overall. First aired on October 16, 2011, it was written by executive story editor Steve Kornacki and directed by Ed Bianchi. Nucky looks to Rothstein for a port to receive alcohol, since the Coast Guard is blockading Atlantic City. Rothstein instructs Lansky and Luciano to oversee the Philadelphia delivery. Nucky also sends Owen Sleater to bomb Doyle's still. Margaret asks for 'money for the children' from Nucky, which she proceeds to hide

title: What Kate Does

text: doesn't quite know how to write a woman of action who's also in love … many of the show's Kate flashbacks are just plain silly … there have been a lot of pretty dire Kate episodes." Whitney Matheson of "USA Today" said that she "wanted to stab Kate with a hot poker" after watching "What Kate Does". Josh Holloway's supporting performance as a grieving Sawyer was commended by Carabott of IGN, who said that his acting on the dock as he cried and revealed to Kate that he was going to ask Juliet to marry him was "one of Josh

title: What Kate Does

text: that it by no means compared to "LA X", but stated that it "contain[ed] scenes of incredible beauty, based on character work and stakes earned over five seasons [that] made it a fine, if imperfect, hour." McGee also commented that the scene in which Claire arrives at the hospital and is helped by Ethan as "freakin' outstanding" and called "What Kate Does" "one of the funniest in the show's history. Aldo, Hurley, and Miles all got off plenty of zingers, which will be necessary in a season in which both mythological and dramatic stakes are raising higher and higher each

title: What Kate Does

text: had hidden and later talks with Kate at Dharma's dock. He explains that he planned to propose to Juliet and that he blames himself for her death, saying that he convinced her to stay on the island with him because he was lonely. Meanwhile, Jin is caught by the Others, who want to kill him instead of taking him back. Suddenly, someone shoots them and Jin is shocked to see that the shooter is Claire. The episode has received mixed reviews. Critical review aggregate website Metacritic awarded "What Kate Does" a score of 64 out of 100, indicating "generally favorable

title: What Does the K Stand For?

text: feel less like real people than excuses to weave in a few good dad jokes". Overall, Elan found, "What lifts the show are the elements of diaspora life weaved throughout, as when Aunty Princess visits from Nigeria and accuses Virginia [Stephen's mother] of cultural betrayal ('You have adopted too many fine and fancy British ways'). Stephen defends the family by suggesting she should 'go back home', prompting him to reflect that he has turned into his own racist enemy. It's unexpectedly thoughtful stuff, suggesting the third series may be even better." What Does the K Stand For? What Does the

title: Measure for Measure

text: Measure for Measure Measure for Measure is a play by William Shakespeare, believed to have been written in 1603 or 1604. Originally published in the "First Folio" of 1623, where it was listed as a comedy, the play's first recorded performance occurred in 1604. The play's main themes include justice, "mortality and mercy in Vienna," and the dichotomy between corruption and purity: "some rise by sin, and some by virtue fall." Mercy and virtue prevail, as the play does not end tragically, with virtues such as compassion and forgiveness being exercised at the end of the production. While the play

title: Angelo (Measure for Measure)

text: the relationship between justice and mercy. There is much debate about what Shakespeare intended this character to portray. Critics disagree about whether Angelo is a good man who has fallen because of power and sexual temptation or a malicious man from the start. Regardless, he is the personification of justice in the play. When juxtaposed against Isabella (mercy), Angelo represents adherence to the law and punishment for sin, though he does not always adhere to the strict justice he enforces. Once Angelo meets Isabella he is forced to consider himself in a different light and acknowledge his shortcomings. "Measure for

title: Measure B

text: a building making decisions for the whole industry. They don't even make decisions on the moratoriums; a doctor does, and she had no idea about that and what the testing protocols—how the doctors work with them to make the most safe tests available; she had no idea. In the thirty-five minute meeting Director Hutt mentioned that in the 2012 election the most votes cast in any district in favor of passage of Measure B came from Hall's district. Actress Nina Hartley countered that although Measure B and AB 1576 were written by policy makers at AIDS Healthcare Foundation, the AHF

title: Does exactly what it says on the tin

text: began a similar copycat advertising campaign in Ireland stating that its product "does exactly what it says on the tube". The phrase is a registered trademark of the Sherwin-Williams Company, the owner of Ronseal, across the European Community for products including paints, varnishes, and wood preservatives (E3085826). In 2007, a song titled "What It Says on the Tin" was released by the British singer Katie Melua. Although the song is about relationships, the phrase has a similar meaning. Does exactly what it says on the tin "It does exactly what it says on the tin" was originally an advertising slogan

title: What Does It Take (To Win Your Love)

text: What Does It Take (To Win Your Love) "What Does It Take (To Win Your Love)" is a 1968 song that was a 1969 hit single by Jr. Walker & The All Stars. The single was one of Jr. Walker's most successful releases, becoming a hit on both the R&B and pop singles charts. "What Does It Take (To Win Your Love)," written by Johnny Bristol, Harvey Fuqua, and Vernon Bullock, made it into the top five on the Hot 100, and became Jr. Walker's second number one on the R&B charts. The song was also a hit in the

title: The Fox (What Does the Fox Say?)

text: neighborhood in Edwards Landing, Leesburg, Virginia, who every Halloween creates an LED light show with a hit song. This song appears in "Just Dance 2015". This song for Leicester City title song parody "What do the Foxes Say?" in 442oons video. !scope="col" colspan="3"| Streaming Note: The Fox (What Does the Fox Say?) "The Fox (What Does the Fox Say?)" is an electronic dance novelty song and viral video by Norwegian comedy duo Ylvis. The top trending video of 2013 on YouTube, "The Fox" was posted on the video-sharing website on 3 September 2013, and has received over 800 million views

title: What Does It Take (To Win Your Love)

text: G (with Ellis Hall on vocals) covered this tune on his 1986 album "Duotones". What Does It Take (To Win Your Love) "What Does It Take (To Win Your Love)" is a 1968 song that was a 1969 hit single by Jr. Walker & The All Stars. The single was one of Jr. Walker's most successful releases, becoming a hit on both the R&B and pop singles charts. "What Does It Take (To Win Your Love)," written by Johnny Bristol, Harvey Fuqua, and Vernon Bullock, made it into the top five on the Hot 100, and became Jr. Walker's second

title: Convex measure

text: Convex measure In measure and probability theory in mathematics, a convex measure is a probability measure that — loosely put — does not assign more mass to any intermediate set “between” two measurable sets "A" and "B" than it does to "A" or "B" individually. There are multiple ways in which the comparison between the probabilities of "A" and "B" and the intermediate set can be made, leading to multiple definitions of convexity, such as log-concavity, harmonic convexity, and so on. The mathematician Christer Borell was a pioneer of the detailed study of convex measures on locally convex spaces in

title: What Does It Take (Dave Days song)

text: What Does It Take (Dave Days song) "What Does It Take" is a song by American singer Dave Days. It served as the third and final single from his 2010 EP "Dinner and a Movie". It is one of Dave's most recognizable songs, and was also played on Disney Channel's So Random!. The song's music video is set in a high school, where Dave realizes he has gotten the lead part in the school play. Amanda Lynn (Days' interest in the video) sees she has gotten the second lead, and runs to her boyfriend, who ignores her. Days and Lynn

title: Content (measure theory)

text: by This is an outer measure, in other words it has the following properties: The function μ above is an outer measure on the family of all subsets. Therefore it becomes a measure when restricted to the measurable subsets for the outer measure, which are the subsets "E" such that μ("X") = μ("X"∩"E") + μ("X"\"E") for all subsets "X". If the space is locally compact then every open set is measurable for this measure. The measure μ does not necessarily coincide with the content λ on compact sets, However it does if λ is regular in the sense that for

title: Resource bounded measure

text: P is a subset of NP, this would mean that NP contains more problems than P. A stronger hypothesis than "P is not NP" is the statement "NP does not have p-measure 0". Here, p-measure is a generalization of Lebesgue measure to subsets of the complexity class E, in which P is contained. P is known to have p-measure 0, and so the hypothesis "NP does not have p-measure 0" would imply not only that NP and P are unequal, but that NP is, in a measure-theoretic sense, "much bigger than P". formula_2 is the set of all infinite, binary

title: The Fox (What Does the Fox Say?)

text: The Fox (What Does the Fox Say?) "The Fox (What Does the Fox Say?)" is an electronic dance novelty song and viral video by Norwegian comedy duo Ylvis. The top trending video of 2013 on YouTube, "The Fox" was posted on the video-sharing website on 3 September 2013, and has received over 800 million views as of November 2018. "The Fox" peaked at the top of the Norwegian Singles Chart and was hugely successful in the United States, where it peaked at number six on the "Billboard" Hot 100 for three consecutive weeks, and was, before the US release of

title: Banach measure

text: this would violate the properties of the Banach measure that extends the Lebesgue measure. The concept of "Banach measure" is to be distinguished from the idea of a measure taking values in a Banach space, for example in the theory of spectral measures. Banach measure In mathematics, Banach measure in measure theory may mean a real-valued function on an algebra of all subsets of a set (for example, all subsets of the plane), by means of which a rigid, finitely additive area can be defined for every set, even when a set does not have a true geometric area. That

title: Carleson measure

text: then the measure "μ" is said to satisfy the vanishing Carleson condition if "C"("R") → 0 as "R" → 0. Carleson measure In mathematics, a Carleson measure is a type of measure on subsets of "n"-dimensional Euclidean space R. Roughly speaking, a Carleson measure on a domain Ω is a measure that does not vanish at the boundary of Ω when compared to the surface measure on the boundary of Ω. Carleson measures have many applications in harmonic analysis and the theory of partial differential equations, for instance in the solution of Dirichlet problems with "rough" boundary. The Carleson condition

title: Banach measure

text: Banach measure In mathematics, Banach measure in measure theory may mean a real-valued function on an algebra of all subsets of a set (for example, all subsets of the plane), by means of which a rigid, finitely additive area can be defined for every set, even when a set does not have a true geometric area. That is, this is a type of generalized measure getting around the phenomenon of non-measurable sets. However, as the Vitali set shows, it cannot be countably additive. A Banach measure on a set Ω is a finite measure μ ≠ 0 on P(Ω), the

title: Carleson measure

text: Carleson measure In mathematics, a Carleson measure is a type of measure on subsets of "n"-dimensional Euclidean space R. Roughly speaking, a Carleson measure on a domain Ω is a measure that does not vanish at the boundary of Ω when compared to the surface measure on the boundary of Ω. Carleson measures have many applications in harmonic analysis and the theory of partial differential equations, for instance in the solution of Dirichlet problems with "rough" boundary. The Carleson condition is closely related to the boundedness of the Poisson operator. Carleson measures are named after the Swedish mathematician Lennart Carleson.

title: Does Anybody Really Know What Time It Is?

text: which also simulcasts in Maine as WJTO 730) plays the original vinyl "" edit. Does Anybody Really Know What Time It Is? "Does Anybody Really Know What Time It Is?" is a song by the rock band Chicago. It was included on their 1969 debut album "Chicago Transit Authority" and released as a single in 1970. The song was written and sung by Robert Lamm. The song was not released as a single until two tracks from the band's second album, "Make Me Smile" and "25 or 6 to 4", had become hits. It became the band's third straight Top

text: Does Anybody Really Know What Time It Is? "Does Anybody Really Know What Time It Is?" is a song by the rock band Chicago. It was included on their 1969 debut album "Chicago Transit Authority" and released as a single in 1970. The song was written and sung by Robert Lamm. The song was not released as a single until two tracks from the band's second album, "Make Me Smile" and "25 or 6 to 4", had become hits. It became the band's third straight Top 10 single, peaking at in the U.S. and No. 2 in Canada. Because the

title: Does exactly what it says on the tin

text: Does exactly what it says on the tin "It does exactly what it says on the tin" was originally an advertising slogan in the United Kingdom, which then became a common idiomatic phrase. It colloquially means that the name of something is an accurate description of its qualities. It is akin to the previously existing phrases "by name and by nature" and "it lives up to its name". It originated in a series of television advertisements by the woodstain and wood-dye manufacturer Ronseal, initiated in 1994 and still being broadcast . The slogan was created by Liz Whiston and Dave

title: What Difference Does It Make?

text: of the Smiths'. The character Ray Smith in the Jack Kerouac novel "The Dharma Bums" repeatedly says "What difference does it make?" as well as "Pretty girls make graves", the title of another track featured on "The Smiths". The single cover is a photograph of Terence Stamp, taken on the set of the film "The Collector". Originally Stamp denied permission for the still to be used, and some pressings featured Morrissey in a re-enacted scene. In the re-enactment, Morrissey is holding a glass of milk, as opposed to a chloroform pad in the original. However, Stamp later changed his mind,

text: life. Poitier explores the nature of sacrifice and commitment, price and humility, rage and forgiveness, and paying the price for artistic integrity. What emerges is a picture of a man in the face of limits; his own as well as the world's. The translation in complicated Chinese () of this autobiography was done by Fongfong Olivia Wei, and published by Triumph Publishing Company in Taipei, Taiwan, in the year 2002. The Measure of a Man: A Spiritual Autobiography The Measure of a Man: A Spiritual Autobiography is an autobiographical work by Sidney Poitier. On January 26, 2007, Oprah Winfrey chose

title: Lebesgue measure

text: not have some curious properties which causes a discrepancy in the measure of another set when formula_6 is used as a "mask" to "clip" that set, hinting at the existence of sets for which the Lebesgue outer measure does not give the Lebesgue measure. (Such sets are, in fact, not Lebesgue-measurable.) The Lebesgue measure on R has the following properties: All the above may be succinctly summarized as follows: The Lebesgue measure also has the property of being "σ"-finite. A subset of R is a "null set" if, for every ε > 0, it can be covered with countably many

title: Cylinder set measure

text: the space of tempered distributions, which extends to a measure on the space of tempered distributions, "S"′. The Hilbert space "H" has measure 0 in "S"′, by the first argument used above to show that the canonical Gaussian cylinder set measure on "H" does not extend to a measure on "H". Cylinder set measure In mathematics, cylinder set measure (or promeasure, or premeasure, or quasi-measure, or CSM) is a kind of prototype for a measure on an infinite-dimensional vector space. An example is the Gaussian cylinder set measure on Hilbert space. Cylinder set measures are in general not measures (and

title: Probability measure

text: of a system S assuming state A is p" the geometry of the system does not always lead to the definition of a probability measure under congruence, although it may do so in the case of systems with just one degree of freedom. Probability measures are also used in mathematical biology. For instance, in comparative sequence analysis a probability measure may be defined for the likelihood that a variant may be permissible for an amino acid in a sequence. Probability measure In mathematics, a probability measure is a real-valued function defined on a set of events in a probability space

title: Radon measure

text: in some sense. One way to do this is to define a measure on the Borel sets of the topological space. In general there are several problems with this: for example, such a measure may not have a well defined support. Another approach to measure theory is to restrict to locally compact Hausdorff spaces, and only consider the measures that correspond to positive linear functionals on the space of continuous functions with compact support (some authors use this as the definition of a Radon measure). This produces a good theory with no pathological problems, but does not apply to spaces

title: Measure S

text: and the quote "I Agree". The other showed a letter written by him on city letterhead, with "I agree" following many pro-Measure S talking points. It was headed "Mayor Garcetti finds a lot to like about Measure S". The mailer implied that Garcetti supported Measure S, which in fact he strongly opposed. He called it a "dirty trick". A CPLA spokesperson said in response that "[t]his was just a friendly reminder on what these City Hall insiders promised and what they've yet to deliver to the voters of Los Angeles." A week before the vote, an editorial in the "Los

title: Spectral risk measure

text: payoff of a portfolio. In this case the translation-invariance property would be given by formula_35 instead of the above. Spectral risk measure A Spectral risk measure is a risk measure given as a weighted average of outcomes where bad outcomes are, typically, included with larger weights. A spectral risk measure is a function of portfolio returns and outputs the amount of the numeraire (typically a currency) to be kept in reserve. A spectral risk measure is always a coherent risk measure, but the converse does not always hold. An advantage of spectral measures is the way in which they can

title: Spectral risk measure

text: Spectral risk measure A Spectral risk measure is a risk measure given as a weighted average of outcomes where bad outcomes are, typically, included with larger weights. A spectral risk measure is a function of portfolio returns and outputs the amount of the numeraire (typically a currency) to be kept in reserve. A spectral risk measure is always a coherent risk measure, but the converse does not always hold. An advantage of spectral measures is the way in which they can be related to risk aversion, and particularly to a utility function, through the weights given to the possible portfolio

title: Cylinder set measure

text: "γ" is the standard Gaussian measure on R. The canonical Gaussian cylinder set measure on an infinite-dimensional separable Hilbert space "H" does not correspond to a true measure on "H". The proof is quite simple: the ball of radius "r" (and center 0) has measure at most equal to that of the ball of radius "r" in an "n"-dimensional Hilbert space, and this tends to 0 as "n" tends to infinity. So the ball of radius "r" has measure 0; as the Hilbert space is a countable union of such balls it also has measure 0, which is a contradiction.

title: Radon measure

text: regular, and locally finite, and inner regular for open sets. It coincides with "m" on compact and open sets, and "m" can be reconstructed from "M" as the unique inner regular measure that is the same as "M" on compact sets. The measure "m" is called moderated if "M" is σ-finite; in this case the measures "m" and "M" are the same. (If "m" is σ-finite this does not imply that "M" is σ-finite, so being moderated is stronger than being σ-finite.) On a strongly Lindelöf space every Radon measure is moderated. An example of a measure "m" that is

title: Signed measure

text: finite signed measure is given by for all "A" in Σ. This signed measure takes only finite values. To allow it to take +∞ as a value, one needs to replace the assumption about "f" being absolutely integrable with the more relaxed condition where "f"("x") = max(−"f"("x"), 0) is the negative part of "f". What follows are two results which will imply that an extended signed measure is the difference of two nonnegative measures, and a finite signed measure is the difference of two finite non-negative measures. The Hahn decomposition theorem states that given a signed measure μ, there exist

title: Alcoholic spirits measure

text: used in Scotland and Northern Ireland. The landlord can chose one or the other but not both. Thimble measures are also used in 175ml and 250ml volumes for measuring wine. Although government stamped for the correct volume, the thimble measure does rely on the user measuring the wine out manually into the thimble. Alcoholic spirits measure Alcoholic spirits measures are instruments designed to measure exact amounts or shots of alcoholic spirits. The most common products used today to measure spirits are the thimble measure and the non-drip measure, often referred to as an optic. The terms "Optic", "Optic Pearl", "OpticJade"

title: Pre-measure

text: is called "σ"-additivity. Thus, what is missing for a pre-measure to be a measure is that it is not necessarily defined on a sigma-algebra (or a sigma-ring). It turns out that pre-measures give rise quite naturally to outer measures, which are defined for all subsets of the space "X". More precisely, if "μ" is a pre-measure defined on a ring of subsets "R" of the space "X", then the set function "μ" defined by is an outer measure on "X" and the measure "μ" induced by "μ" on the σ-algebra Σ of Carathéodory-measurable sets satisfies formula_4 for formula_5 (in particular,

title: Field Music (Measure)

text: Do Nothing" and "Let's Write A Book"), whilst the second disc is dominated by more experimental tracks including found-sound pieces ("See You Later" and "Louis"). <br> Field Music (Measure) Field Music (Measure) is the third full-length studio album by indie rock band Field Music. It was released on 15 February 2010. Officially, the album's name is the same as their debut album; the name "Measure", other than being the name of one of the songs, does not appear anywhere on the album's artwork. However, both fans and the band have taken to calling it "Measure" to distinguish the two. "Measure"

title: Field Music (Measure)

text: Field Music (Measure) Field Music (Measure) is the third full-length studio album by indie rock band Field Music. It was released on 15 February 2010. Officially, the album's name is the same as their debut album; the name "Measure", other than being the name of one of the songs, does not appear anywhere on the album's artwork. However, both fans and the band have taken to calling it "Measure" to distinguish the two. "Measure" is a double album and is split into two discs. The first disc primarily contains more traditionally-structured songs, including both of the album's singles ("Them That

title: Resource bounded measure

text: of sequences has p-measure 0 if there is a "polynomial-time computable" martingale that succeeds on the set. We define a set to have p-measure 1 if its complement has p-measure 0. For example, proving the above-mentioned conjecture, that NP does not have p-measure 0, amounts to proving that no polynomial-time martingale succeeds on all of NP. A problem is almost complete for a complexity class C if it is in C and "many" other problems in C reduce to it. More specifically, the subset of problems of C which reduce to the problem is a measure one set, in terms

title: Jordan measure

text: finite union and intersection of Jordan measurable sets is Jordan measurable, as well as the set difference of any two Jordan measurable sets. A compact set is not necessarily Jordan measurable. For example, the fat Cantor set is not. Its inner Jordan measure vanishes, since its complement is dense; however, its outer Jordan measure does not vanish, since it cannot be less than (in fact, is equal to) its Lebesgue measure. Also, a bounded open set is not necessarily Jordan measurable. For example, the complement of the fat Cantor set (within the interval) is not. A bounded set is Jordan

title: What Does the K Stand For?

text: sitcom". Writing in "The Guardian" in February 2015, Priya Elan judged that, "Standup comedian Stephen K Amos's jaunty sitcom "What Does The K Stand For?" (Radio 4) reaches the end of its second series with possibly the best episode yet. With shades of Chris Rock's "Everybody Hates Chris", Amos takes us back to his 80s childhood, growing up gay and black in a dysfunctional household". However, he added, "Playing it broad by mixing farce with double entendres, the sitcom is slightly uneven: although the family are drawn with wit and sympathy, minor characters like the actress turned teacher Miss Bliss

title: Convergence in measure

text: formula_14, "μ" be Lebesgue measure, and "f" the constant function with value zero. (The first five terms of which are formula_19) converges to "0" globally in measure; but for no "x" does "f(x)" converge to zero. Hence "(f)" fails to converge to "f" almost everywhere. There is a topology, called the topology of (local) convergence in measure, on the collection of measurable functions from "X" such that local convergence in measure corresponds to convergence on that topology. This topology is defined by the family of pseudometrics where In general, one may restrict oneself to some subfamily of sets "F" (instead

title: Individual Deprivation Measure

text: action. The IDM can help governments and organisations target poverty more effectively as well as help them measure success or failure, revealing what aspects of poverty are changing, by how much and for whom. The IDM is the first poverty measure in the world based on the views of women and men with lived experience of poverty. The dimensions were informed by how women and men think poverty should be defined and what needs to improve in order to move out of poverty. The first research phase of the Individual Deprivation Measure started in 2009. It was a four-year, international,

title: What Kate Does

text: Does' slows the pace down significantly from last week and focuses on telling a character-driven story. This is a welcome change; especially after the heavily plot-driven season five. However, with questions to answer and so much ground to cover during this final season, a better balance between plot and character wouldn't have been such a bad thing." Alan Sepinwall of "The Star-Ledger" wrote, "Maybe I'll enjoy the 2004 scenes more when we get to some other characters … but this week it was largely a distraction from all that was happening on the island. And even the island scenes were

title: What Kate Does

text: Does", stating that "Episodes like this one can make real "Lost" fans feel like dopes. Already, you're taking heaps of abuse from friends who accuse you of slavishly following a series which makes no sense—then along comes a 60-minute workout like this one which proves their point all too well." Daniel of TMZ, who gave the episode a "D" grade, reacted uniquely with "The only thing in the history of "Lost" that has seemed more out of place than the part in Jack's hair was Nikki and Paulo. I can't take anything he says seriously." Ryan McGee of Zap2it stated

title: Tangent measure

text: ball of radius "r" around "a", "B"("a"), via the transformation which enlarges the ball of radius "r" about "a" to a ball of radius 1 centered at 0. With this, we may now zoom in on how "μ" behaves on "B"("a") by looking at the push-forward measure defined by where As "r" gets smaller, this transformation on the measure "μ" spreads out and enlarges the portion of "μ" supported around the point "a". We can get information about our measure around "a" by looking at what these measures tend to look like in the limit as "r" approaches zero. The

title: Tape measure

text: cases, spring return pocket tape measures and long tape measures. Spring return pocket tape measures will generally fit in a pocket. They are small, the case is up to about three inches across. The tape is returned to the case by a spring mechanism. Pocket tape measures have a tape one foot to fifteen feet in length and ¼ to ¾ inches across. When most people think of a tape measure, they are thinking of the pocket tape measure. A second tape measure design is what is called the long tape. These are cased tape measures with tapes of 25,

title: Measure S

text: housing, that local labor be used on them, and incentivized developers for building near the city's subway lines. The city's business community, particularly developers, were as opposed to it as they were to Measure S. However, so was the CPLA. In a news release strongly opposing JJJ, it claimed that initiative had been "cooked up" by the interests opposing Measure S in an effort to split its support and keep it from the ballot. Measure S proponents said that they considered JJJ likely to fall short of its goals, pointing to what they considered broadly worded loopholes in JJJ. "Ultimately

title: Measure S

text: that increase to what it said were thousands of evictions of rent-stabilized tenants by developers looking to build the high-density luxury housing Measure S was meant to curtail, endorsed Measure HHH, a bond issue on the upcoming ballot that would raise $1.2 billion and commit it to buying property on which facilities for the homeless would be built. Both sides on Measure S were primarily composed of liberals and progressives, often in ethnic or social groups that identified politically with the Democratic Party, which overwhelmingly dominates politics in Los Angeles. As such, supporters and opponents of the initiative compared the

title: The Fox (What Does the Fox Say?)

text: Bay. The video is produced by Fredrik Kvåle Dørum and Jørgen Thue (Concorde TV). The forest scenes were filmed in Nittedal municipality, from Oslo downtown. The video begins with Bård singing at a costume party where other participants are dressed as different animals, whose appearances follow the progression of the lyrics. He gives a summary of animal sounds ("Dog goes woof/cat goes meow", etc.) that "could have been lifted straight from a preschool primer" and asks "what does the fox say?" The group then transitions into a synchronized dance scene in a forest with Bård in a bear costume and

title: What Does It Take (Dave Days song)

text: to attack the cast and crew, along with himself. The cast fends off the kids, and its down to the boyfriend and Days. An audience member throws Dave his guitar. Dave blocks a hit from a sword the boyfriend is carrying, and knocks him to the ground by hitting him with the head of the guitar while doing a guitar flip. He then takes the sword he had and puts it to his neck while he is on the ground. The audience then claps, and Days and Lynn hug and wave to the crowd. What Does It Take (Dave Days

title: The Fox (What Does the Fox Say?)

text: "YouTube Rewind: What Does 2013 Say?", a homage paid by YouTube to the year's top videos. The song has been featured for multiple times on television. It was used in an advertisement for the Fox Network featuring clips of FOX programs and actors singing the song. On 28 October, four contestants on the seventeenth season of "Dancing with the Stars" performed the song for the "Team Dance" week under the team name "Foxing Awesome", scoring a perfect 30. NBC's "Saturday Night Live" cast-member Jay Pharoah and host Kerry Washington appeared in a parody video of the song titled "My Girl"

title: The Fox (What Does the Fox Say?)

text: did not know about its existence when producing "The Fox". Like many viral music videos, "The Fox" has become an Internet meme and has been extensively covered and adapted by others, with some of the most prominent being a cover by The Ohio University Marching 110 who had previously covered "Gangnam Style" and LMFAO's "Party Rock Anthem"; a cover by Tay Zonday of "Chocolate Rain"; an acoustic guitar cover of the first verse by Tyler Ward; an adaptation based on the popular video game "League of Legends" entitled "What Does Teemo Say?"; and an adaptation by Annoying Orange entitled "The

title: Curvature of a measure

text: the integral is taken only over those points "x", "y" and "z" such that Similarly, formula_11 denotes a truncated Cauchy integral operator: for a measure "μ" on C and a point "z" in C, define where the integral is taken over those points "ξ" in C with Curvature of a measure In mathematics, the curvature of a measure defined on the Euclidean plane R is a quantification of how much the measure's "distribution of mass" is "curved". It is related to notions of curvature in geometry. In the form presented below, the concept was introduced in 1995 by the mathematician

title: Curvature of a measure

text: Curvature of a measure In mathematics, the curvature of a measure defined on the Euclidean plane R is a quantification of how much the measure's "distribution of mass" is "curved". It is related to notions of curvature in geometry. In the form presented below, the concept was introduced in 1995 by the mathematician Mark S. Melnikov; accordingly, it may be referred to as the Melnikov curvature or Menger-Melnikov curvature. Melnikov and Verdera (1995) established a powerful connection between the curvature of measures and the Cauchy kernel. Let "μ" be a Borel measure on the Euclidean plane R. Given three (distinct)

title: Measure B

text: wear condoms during porn shoots does not violate the First Amendment, enforcing such a law raises constitutional questions, and denied the adult film industry's motion for a preliminary injunction. Judge Pregerson agreed that some of the provisions and language of measure were too vague and did not sufficiently explain condom use when other sex acts were being filmed. He also questioned the manner of inspections to be conducted and agreed with the industry that their rights could be violated. Pregerson wrote, "Given that adult filming could occur almost anywhere, Measure B would seem to authorize a health officer to enter

title: Haar measure

text: nontrivial but the modular function of formula_3 is trivial. The quotient of these cannot be extended to any character of formula_3, so the quotient space formula_114 (which can be thought of as 1-dimensional real projective space) does not have even a semi-invariant measure. Using the general theory of Lebesgue integration, one can then define an integral for all Borel measurable functions formula_84 on formula_3. This integral is called the Haar integral. If formula_11 is a left Haar measure, then for any Haar integrable function formula_84 on formula_3. This is immediate for indicator functions, being essentially the definition of left invariance.

title: Haar measure

text: invariant measure for second countable locally compact groups had been shown by Haar in 1933. The following method of constructing Haar measure is essentially the method used by Haar and Weil. For any subsets formula_48 with formula_6 nonempty define formula_50 to be the smallest number of left translates of formula_6 that cover formula_52 (so this is a non-negative integer or infinity). This is not additive on compact sets formula_29, though it does have the property that formula_54 for disjoint compact sets formula_55 provided that formula_56 is a sufficiently small open neighborhood of the identity (depending on formula_57 and formula_58). The