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A note on the density of $s$-dimensional sets

Author: James Foran
Journal: Proc. Amer. Math. Soc. 126 (1998), 863-865
MSC (1991): Primary 28A78
MathSciNet review: 1452803
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Abstract: Sets in Euclidean spaces which are measurable with respect to Hausdorff $s$-dimensional measure with $0<s<1$ are shown to have an at most countable set of points where the exact $s$-density exists and is finite and non-zero.

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

  • 1. K. J. Falconer, The Geometry of Fractal Sets, Cambridge Univ. Press, 1985. MR 88d:28001
  • 2. J. M. Marstrand, Some fundamental properties of plane sets of fractional dimension, Proc. Lond. Math. Soc. (3) 4 (1954), 257-302. MR 16:121g

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Additional Information

James Foran
Affiliation: Department of Mathematics, University of Missouri-Kansas City, Kansas City, Missouri 64110

Received by editor(s): September 14, 1996
Communicated by: James West
Article copyright: © Copyright 1998 American Mathematical Society

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