An optimization of the Besicovitch covering
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- by Peter A. Loeb PDF
- Proc. Amer. Math. Soc. 118 (1993), 715-716 Request permission
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
- A. S. Besicovitch, A general form of the covering principle and relative differentiation of additive functions, Proc. Cambridge Philos. Soc. 41 (1945), 103–110. MR 12325, DOI 10.1017/s0305004100022453
- Albert E. Hurd and Peter A. Loeb, An introduction to nonstandard real analysis, Pure and Applied Mathematics, vol. 118, Academic Press, Inc., Orlando, FL, 1985. MR 806135
- Peter A. Loeb, On the Besicovitch covering theorem, SUT J. Math. 25 (1989), no. 1, 51–55. MR 1049602
Additional Information
- © Copyright 1993 American Mathematical Society
- 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