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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An optimization of the Besicovitch covering


Author: Peter A. Loeb
Journal: Proc. Amer. Math. Soc. 118 (1993), 715-716
MSC: Primary 03H05; Secondary 28A75, 28E05, 52C17, 54J05
MathSciNet review: 1132415
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Abstract: Given an appropriate covering by balls of a set in a metric space, we construct an optimized version of the subcovering used in the proof of Besicovitch's theorem. The proof is nonstandard and suggests a general method for optimizing standard geometric constructions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1132415-7
PII: S 0002-9939(1993)1132415-7
Keywords: Besicovitch, optimized covering, nonstandard analysis
Article copyright: © Copyright 1993 American Mathematical Society