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Density points and bi-Lipschitz functions in $\textbf {R}^ m$


Author: Zoltán Buczolich
Journal: Proc. Amer. Math. Soc. 116 (1992), 53-59
MSC: Primary 26B35; Secondary 54C30
DOI: https://doi.org/10.1090/S0002-9939-1992-1100645-5
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?)

  • Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York Inc., New York, 1969. MR 0257325
  • Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
  • 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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Article copyright: © Copyright 1992 American Mathematical Society