Em matemática, sobretudo na teoria da medida, funções mensuráveis são aquelas que apresentam comportamento suficientemente simples para que se possa desenvolver uma teoria de integração.

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  • Em matemática, sobretudo na teoria da medida, funções mensuráveis são aquelas que apresentam comportamento suficientemente simples para que se possa desenvolver uma teoria de integração.
  • En teoría de la medida, una función medible es aquella que preserva la estructura entre dos espacios medibles. Formalmente, una función entre dos espacios medibles se dice medible si la preimagen (también llamada imagen inversa) de cualquier conjunto medible es a su vez medible.
  • In mathematics, particularly in measure theory, measurable functions are structure-preserving functions between measurable spaces; as such, they form a natural context for the theory of integration. Specifically, a function between measurable spaces is said to be measurable if the preimage of each measurable set is measurable, analogous to the situation of continuous functions between topological spaces.This definition can be deceptively simple, however, as special care must be taken regarding the σ-algebras involved. In particular, when a function f: R → R is said to be Lebesgue measurable what is actually meant is that is a measurable function—that is, the domain and range represent different σ-algebras on the same underlying set (here is the sigma algebra of Lebesgue measurable sets, and is the Borel algebra on R). As a result, the composition of Lebesgue-measurable functions need not be Lebesgue-measurable.By convention a topological space is assumed to be equipped with the Borel algebra generated by its open subsets unless otherwise specified. Most commonly this space will be the real or complex numbers. For instance, a real-valued measurable function is a function for which the preimage of each Borel set is measurable. A complex-valued measurable function is defined analogously. In practice, some authors use measurable functions to refer only to real-valued measurable functions with respect to the Borel algebra. If the values of the function lie in an infinite-dimensional vector space instead of R or C, usually other definitions of measurability are used, such as weak measurability and Bochner measurability.In probability theory, the sigma algebra often represents the set of available information, and a function (in this context a random variable) is measurable if and only if it represents an outcome that is knowable based on the available information. In contrast, functions that are not Lebesgue measurable are generally considered pathological, at least in the field of analysis.
  • In analisi matematica, una funzione misurabile è un'applicazione tra due spazi misurabili compatibile con la loro struttura di σ-algebra.La richiesta di misurabilità di una funzione è in genere un'ipotesi di regolarità minima, ed è molto spesso richiesta per l'applicazione dei teoremi e dei metodi dell'analisi matematica e della teoria della misura.
  • Измери́мые функции представляют естественный класс функций, связывающих пространства с выделенными алгебрами, в частности измеримыми пространствами.
  • 측도론에서, 가측함수(可測函數, 영어: measurable function) 또는 측정가능한 함수는 두 측도공간 사이에 정의되는 함수로, 집합의 가측성을 보존하는 함수를 의미한다.
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  • Em matemática, sobretudo na teoria da medida, funções mensuráveis são aquelas que apresentam comportamento suficientemente simples para que se possa desenvolver uma teoria de integração.
  • En teoría de la medida, una función medible es aquella que preserva la estructura entre dos espacios medibles. Formalmente, una función entre dos espacios medibles se dice medible si la preimagen (también llamada imagen inversa) de cualquier conjunto medible es a su vez medible.
  • In analisi matematica, una funzione misurabile è un'applicazione tra due spazi misurabili compatibile con la loro struttura di σ-algebra.La richiesta di misurabilità di una funzione è in genere un'ipotesi di regolarità minima, ed è molto spesso richiesta per l'applicazione dei teoremi e dei metodi dell'analisi matematica e della teoria della misura.
  • Измери́мые функции представляют естественный класс функций, связывающих пространства с выделенными алгебрами, в частности измеримыми пространствами.
  • 측도론에서, 가측함수(可測函數, 영어: measurable function) 또는 측정가능한 함수는 두 측도공간 사이에 정의되는 함수로, 집합의 가측성을 보존하는 함수를 의미한다.
  • In mathematics, particularly in measure theory, measurable functions are structure-preserving functions between measurable spaces; as such, they form a natural context for the theory of integration.
rdfs:label
  • Fonction mesurable
  • Funció mesurable
  • Función medible
  • Funkcja mierzalna
  • Funzione misurabile
  • Função mensurável
  • Measurable function
  • Meetbare functie
  • Messbare Funktion
  • Měřitelná funkce
  • Измеримая функция
  • 可測関数
  • 가측함수
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