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Lipschitz continuity
Lipschitz continuity In mathematics, a function f : I → ... real numbers with real values is called Lipschitz continuous (or is said to satisfy a Lipschitz condition) if there exists a constant K ... The smallest such K is called the Lipschitz constant of the function in that ...
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Uniform continuity
Uniform continuity In mathematical analysis, a function f(x ... small changes in the output f(x) ("continuity"), and furthermore the size of the changes ... x but not on x itself ("uniformity"). Continuity itself is a local property of a ... point of the interval. In contrast, uniform continuity is a global property of a function ... is uniformly continuous on that interval. Every Lipschitz continuous map between two metric spaces ...
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Rudolf Lipschitz
Rudolf Lipschitz Rudolf Otto Sigismund Lipschitz (May 14, 1832 – October 7, 1903 ... supervised the early work of Felix Klein. Lipschitz gave his name to the Lipschitz continuity condition; in fact he worked in ...
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Absolute continuity
Absolute continuity Absolute continuity of real functions In mathematics, a real ... is uniformly continuous and, therefore, continuous. Every Lipschitz-continuous function is absolutely continuous. The Cantor ... continuous everywhere but not absolutely continuous. Absolute continuity of measures If μ and ν are ... d\nu. The connection between absolute continuity of real functions and absolute continuity ...
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Uniform continuity (translated from Dutch)
Uniform continuity In wiskunde one speak of uniformly ongoing ... the value of x itself. Consequently uniform continuity is rather an overall property of a ... of x. Definition Formally one can uniform continuity define using so-called ` epsilon-delta'-definitie ... ongoing function are also uniform ongoing. Each Lipschitz-continue function is also uniform ongoing.
http://nl.wikipedia.org/wiki/Uniforme_continuïteit - 2k - Cached (Dutch) - Wikipedia (Dutch) - Similar pages
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Absolute continuity (translated from Dutch)
Absolute continuity In wiskunde , reëel -worthy function f is ... and for this reason tevens continu . Each Lipschitz-continue functie are absolutely ongoing. Cantorfunctie is ...
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Continuous Lipschitz (translated from Spanish)
Continuous Lipschitz In mathematical, one función f : M → ... M and N it is called Continuous Lipschitz (or one says that it satisfies one condition of Lipschitz) if a constant exists K > 0 so ... In such case, K it is called Lipschitz constant of the function. The name comes from mathematician alemán Rudolf Lipschitz. All continuous Lipschitz function is uniformly ...
http://es.wikipedia.org/wiki/Lipschitz_continua - 3k - Cached (Spanish) - Wikipedia (Spanish) - Similar pages
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Absolute continuity (translated from Italian)
Absolute continuity Absolute continuity of the real functions In matematica , one ... it continues and, consequently, continua . Every function Lipschitz-continues it is absolutely continuous. function of ... but it is not absolutely continuous. Absolute continuity of the measures If? and? they are ... f\, d\nu . Connection between absolute continuity of the real functions and the ...
http://it.wikipedia.org/wiki/Continuità_assoluta - 3k - Cached (Italian) - Wikipedia (Italian) - Similar pages
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Uniform continuity (translated from Italian)
Uniform continuity In analisi , one funzione uniform it continues ... point same. The uniform continuity is therefore a total property of the function, contrarily to the simple continuity that is one local property. In fact ... x_2)| < \epsilon. Various from the simple continuity the distance it only ... of Heine - Cantor it asserts that the continuity is equivalent to the uniform continuity. ...
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Modulus of continuity
Modulus of continuity In mathematics, the modulus of continuity is a precise way to measure the ... Similar but less refined notions such as Lipschitz continuity and Hölder class are subsumed by the explicit use of the modulus of continuity. Above and below we use the ...
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