Besicovitch covering theorem
- Besicovitch covering theorem
In mathematical analysis, a Besicovitch cover is an open cover of a subset "E" of the Euclidean space R"N" 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 "c"N depending only on the dimension "N" with the following property:
* Given any Besicovitch cover F of a bounded set "E", there are "c""N" subcollections of balls "A"1={"B""n"1}, …, "A""c""N"={"B""n""c""N"} contained in F such that each collection "A"i consists of disjoint balls, and:
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