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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
DOI: https://doi.org/10.1090/S0002-9939-1993-1132415-7
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.


References [Enhancements On Off] (What's this?)

  • [1] A. S. Besicovitch, A general form of the covering principle and relative differentiation of additive functions I, Proc. Cambridge Philos. Soc. 41 (1945), 103-110; II, 42 (1946), 1-10. MR 0012325 (7:10e)
  • [2] A. E. Hurd and P. A. Loeb, An introduction to nonstandard real analysis, Pure Appl. Math., vol. 118, Academic Press, Orlando, FL, 1985. MR 806135 (87d:03184)
  • [3] P. A. Loeb, On the Besicovitch covering theorem, Tokyo J. Math 25 (1989). 51-55. MR 1049602 (91c:28003)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1132415-7
Keywords: Besicovitch, optimized covering, nonstandard analysis
Article copyright: © Copyright 1993 American Mathematical Society

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