Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Density points and bi-Lipschitz functions in $ {\bf R}\sp m$


Author: Zoltán Buczolich
Journal: Proc. Amer. Math. Soc. 116 (1992), 53-59
MSC: Primary 26B35; Secondary 54C30
MathSciNet review: 1100645
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Abstract: If $ A,B \subset {{\mathbf{R}}^m}$ and $ f$ is a bi-Lipschitz function mapping $ A$ onto $ B$ then density or dispersion points of $ A$ are mapped exactly onto density or dispersion points of $ B$, respectively.


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

  • [F] Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325
  • [HW] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
  • [R] Walter Rudin, Functional analysis, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. McGraw-Hill Series in Higher Mathematics. MR 0365062

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1100645-5
Article copyright: © Copyright 1992 American Mathematical Society