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- Besicovitch_covering_theorem abstract "In mathematical analysis, a Besicovitch cover, named after Abram Samoilovitch Besicovitch, is an open cover of a subset E of the Euclidean space RN by balls such that each point of E is the center of some ball in the cover.The Besicovitch covering theorem asserts that there exists a constant cN depending only on the dimension N with the following property: Given any Besicovitch cover F of a bounded set E, there are cN subcollections of balls A1 = {Bn1}, …, AcN = {BncN} contained in F such that each collection Ai consists of disjoint balls, andLet G denote the subcollection of F consisting of all balls from the cN disjoint families A1,...,AcN.The less precise following statement is clearly true: every point x ∈ RN belongs to at most cN different balls from the subcollection G, and G remains a cover for E (every point y ∈ E</sup> belongs to at least one ball from the subcollection G). This property gives actually an equivalent form for the theorem (except for the value of the constant). There exists a constant bN depending only on the dimension N with the following property: Given any Besicovitch cover F of a bounded set E, there is a subcollection G of F such that G is a cover of the set E and every point x ∈ RN belongs to at most bN different balls from the subcover G.In other words, the function SG equal to the sum of the indicator functions of the balls in G is larger than 1E and bounded on RN by the constant bN,".
- Besicovitch_covering_theorem wikiPageID "17743903".
- Besicovitch_covering_theorem wikiPageRevisionID "578750266".
- Besicovitch_covering_theorem hasPhotoCollection Besicovitch_covering_theorem.
- Besicovitch_covering_theorem subject Category:Covering_lemmas.
- Besicovitch_covering_theorem subject Category:Theorems_in_analysis.
- Besicovitch_covering_theorem type Abstraction100002137.
- Besicovitch_covering_theorem type Communication100033020.
- Besicovitch_covering_theorem type CoveringLemmas.
- Besicovitch_covering_theorem type Lemma106751833.
- Besicovitch_covering_theorem type Message106598915.
- Besicovitch_covering_theorem type Proposition106750804.
- Besicovitch_covering_theorem type Statement106722453.
- Besicovitch_covering_theorem type Theorem106752293.
- Besicovitch_covering_theorem type TheoremsInAnalysis.
- Besicovitch_covering_theorem comment "In mathematical analysis, a Besicovitch cover, named after Abram Samoilovitch Besicovitch, is an open cover of a subset E of the Euclidean space RN by balls such that each point of E is the center of some ball in the cover.The Besicovitch covering theorem asserts that there exists a constant cN depending only on the dimension N with the following property: Given any Besicovitch cover F of a bounded set E, there are cN subcollections of balls A1 = {Bn1}, …, AcN = {BncN} contained in F such that each collection Ai consists of disjoint balls, andLet G denote the subcollection of F consisting of all balls from the cN disjoint families A1,...,AcN.The less precise following statement is clearly true: every point x ∈ RN belongs to at most cN different balls from the subcollection G, and G remains a cover for E (every point y ∈ E</sup> belongs to at least one ball from the subcollection G). ".
- Besicovitch_covering_theorem label "Besicovitch covering theorem".
- Besicovitch_covering_theorem label "Лемма Безиковича".
- Besicovitch_covering_theorem label "ベシコビッチの被覆定理".
- Besicovitch_covering_theorem label "貝西科維奇覆蓋定理".
- Besicovitch_covering_theorem sameAs ベシコビッチの被覆定理.
- Besicovitch_covering_theorem sameAs m.047fh0z.
- Besicovitch_covering_theorem sameAs Q137164.
- Besicovitch_covering_theorem sameAs Q137164.
- Besicovitch_covering_theorem sameAs Besicovitch_covering_theorem.
- Besicovitch_covering_theorem wasDerivedFrom Besicovitch_covering_theorem?oldid=578750266.
- Besicovitch_covering_theorem isPrimaryTopicOf Besicovitch_covering_theorem.