Absolute continuity
In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity. The notion of absolute continuity allows one to obtain generalizations of the relationship between the two central operations of calculus, differentiation and integration, expressed by the fundamental theorem of calculus in the framework of Riemann integration. Such generalizations are often formulated in terms of Lebesgue integration. For real-valued functions on the real line two interrelated notions appear: absolute continuity of functions and absolute continuity of measures. These two notions are generalized in different directions. The usual derivative of a function is related to the Radon–Nikodym derivative, or density, of a measure.
primaryTopic
Absolute continuity
In calculus, absolute continuity is a smoothness property of functions that is stronger than continuity and uniform continuity. The notion of absolute continuity allows one to obtain generalizations of the relationship between the two central operations of calculus, differentiation and integration, expressed by the fundamental theorem of calculus in the framework of Riemann integration. Such generalizations are often formulated in terms of Lebesgue integration. For real-valued functions on the real line two interrelated notions appear: absolute continuity of functions and absolute continuity of measures. These two notions are generalized in different directions. The usual derivative of a function is related to the Radon–Nikodym derivative, or density, of a measure.
has abstract
Ciągłość bezwzględna, absolutn ...... zwaną również gęstością miary.
@pl
En mathématiques, et plus préc ...... de mesure absolument continue.
@fr
In calculus, absolute continui ...... fferentiable almost everywhere
@en
In de wiskundige analyse wordt ...... text van de Lebesgue-maat op .
@nl
In der Analysis ist die absolu ...... erung von Lebesgue-Integralen.
@de
In matematica, il concetto di continuità assoluta si applica a due concetti distinti.
@it
Абсолютная непрерывность — в м ...... производной Радона — Никодима.
@ru
在数学中，绝对连续是一个光滑性质，比连续和一致连续都要严格。函数的绝对连续和测度的绝对连续都有定义。
@zh
数学における絶対連続（ぜったいれんぞく、英: absolut ...... しているが見かけ上異なるふたつの絶対連続性の定義がなされる。
@ja
Link from a Wikipage to an external page
Wikipage page ID
Wikipage revision ID
742,383,728
hypernym
type
comment
Ciągłość bezwzględna, absolutn ...... zwaną również gęstością miary.
@pl
En mathématiques, et plus préc ...... de mesure absolument continue.
@fr
In calculus, absolute continui ...... ive, or density, of a measure.
@en
In de wiskundige analyse wordt ...... text van de Lebesgue-maat op .
@nl
In der Analysis ist die absolu ...... erung von Lebesgue-Integralen.
@de
In matematica, il concetto di continuità assoluta si applica a due concetti distinti.
@it
Абсолютная непрерывность — в м ...... производной Радона — Никодима.
@ru
在数学中，绝对连续是一个光滑性质，比连续和一致连续都要严格。函数的绝对连续和测度的绝对连续都有定义。
@zh
数学における絶対連続（ぜったいれんぞく、英: absolut ...... しているが見かけ上異なるふたつの絶対連続性の定義がなされる。
@ja
label
Absolue continuité
@fr
Absolut stetige Funktion
@de
Absolute continuity
@en
Absolute continuïteit
@nl
Ciągłość bezwzględna
@pl
Continuità assoluta
@it
Абсолютная непрерывность
@ru
絶対連続
@ja
绝对连续
@zh