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

Author(s): James Foran
Journal: Proc. Amer. Math. Soc. 126 (1998), 863-865.
MSC (1991): Primary 28A78
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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:

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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