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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 Tracts in Mathematics, vol. 85, Cambridge University Press, Cambridge, 1986. MR 867284
  • 2. J. M. Marstrand, Some fundamental geometrical properties of plane sets of fractional dimensions, Proc. London Math. Soc. (3) 4 (1954), 257–302. MR 0063439

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Additional Information

James Foran
Affiliation: Department of Mathematics, University of Missouri-Kansas City, Kansas City, Missouri 64110
Email: jforan@cctr.umkc.edu

DOI: https://doi.org/10.1090/S0002-9939-98-04384-6
Received by editor(s): September 14, 1996
Communicated by: James West
Article copyright: © Copyright 1998 American Mathematical Society