Lebesgue's density theorem
In mathematics, Lebesgue's density theorem states that for any Lebesgue measurable set , the "density" of A is 0 or 1 at almost every point in . Additionally, the "density" of A is 1 at almost every point in A. Intuitively, this means that the "edge" of A, the set of points in A whose "neighborhood" is partially in A and partially outside of A, is negligible. Let μ be the Lebesgue measure on the Euclidean space Rn and A be a Lebesgue measurable subset of Rn. Define the approximate density of A in a ε-neighborhood of a point x in Rn as where Bε denotes the closed ball of radius ε centered at x.
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Lebesgue's density theorem
In mathematics, Lebesgue's density theorem states that for any Lebesgue measurable set , the "density" of A is 0 or 1 at almost every point in . Additionally, the "density" of A is 1 at almost every point in A. Intuitively, this means that the "edge" of A, the set of points in A whose "neighborhood" is partially in A and partially outside of A, is negligible. Let μ be the Lebesgue measure on the Euclidean space Rn and A be a Lebesgue measurable subset of Rn. Define the approximate density of A in a ε-neighborhood of a point x in Rn as where Bε denotes the closed ball of radius ε centered at x.
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In matematica, il teorema di d ...... olare del teorema di Lebesgue.
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In mathematics, Lebesgue's den ...... esgue measure, see Discussion.
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Twierdzenie Lebesgue’a o punkt ...... dzenie Bezikowicza o pokryciu.
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Теорема Лебега про щільність — ...... имірної множини має міру нуль.
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Теорема о точках плотности — р ...... ого множества имеет меру ноль.
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数学におけるルベーグの密度定理は、任意のルベーグ可測集合 A ...... ルベーグの密度定理は、ルベーグの微分定理の特殊な場合である。
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수학에서 르베그 밀도 정리는 임의의 밀도 측도 집합 A ...... A에서의 거의 모든 점들의 밀도 는 존재하며, 1이다.
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title
Lebesgue density theorem
@en
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comment
In matematica, il teorema di d ...... olare del teorema di Lebesgue.
@it
In mathematics, Lebesgue's den ...... all of radius ε centered at x.
@en
Twierdzenie Lebesgue’a o punkt ...... dzenie Bezikowicza o pokryciu.
@pl
Теорема Лебега про щільність — ...... имірної множини має міру нуль.
@uk
Теорема о точках плотности — р ...... ого множества имеет меру ноль.
@ru
数学におけるルベーグの密度定理は、任意のルベーグ可測集合 A ...... と）は空ではないが、（零集合になるという意味で）無視できる。
@ja
수학에서 르베그 밀도 정리는 임의의 밀도 측도 집합 A ...... A에서의 거의 모든 점들의 밀도 는 존재하며, 1이다.
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Dichtheidsstelling van Lebesgue
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Lebesgue's density theorem
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Teorema di densità di Lebesgue
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Twierdzenie Lebesgue’a o punktach gęstości
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Теорема Лебега про щільність
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Теорема о точках плотности
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ルベーグの密度定理
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르베그 밀도 정리
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