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A note on the density of  -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  -dimensional measure with  are shown to have an at most countable set of points where the exact  -density exists and is finite and non-zero.
- 1.
K.
J. Falconer, The geometry of fractal sets, Cambridge Tracts in
Mathematics, vol. 85, Cambridge University Press, Cambridge, 1986. MR 867284
(88d:28001)
- 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
(16,121g)
- 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
Email:
jforan@cctr.umkc.edu
DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04384-6
PII:
S 0002-9939(98)04384-6
Received by editor(s):
September 14, 1996
Communicated by:
James West
Article copyright:
© Copyright 1998 American Mathematical Society
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