Billingsley's packing dimension
Author:
Manav Das
Journal:
Proc. Amer. Math. Soc. 136 (2008), 273278
MSC (2000):
Primary 28A78, 28A80
Published electronically:
October 18, 2007
MathSciNet review:
2350413
Fulltext PDF Free Access
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Abstract: For a stochastic process on a finite state space, we define the notion of a packing measure based on the naturally defined cylinder sets. For any two measures , , corresponding to the same stochastic process, if then we prove that
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 Manabendra Das, Pointwise Local Dimensions, Ph. D. Thesis, The Ohio State University, 1996.
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 Manav Das, Packing Measures, Dimensions and Mutual Singularity, preprint.
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 Manav Das, Hausdorff Measures, Dimensions and Mutual Singularity, Trans. Amer. Math. Soc, 357, no. 11, 2005, pp. 42494268 MR 2156710 (2006g:28010)
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 S. James Taylor, The measure theory of random fractals, Math. Proc. Cambridge Philos. Soc., 100, no. 3, 1986, pp. 383406. MR 857718 (87k:60189)
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Additional Information
Manav Das
Affiliation:
Department of Mathematics, 328 Natural Sciences Building, University of Louisville, Louisville, Kentucky 40292
Email:
manav@louisville.edu
DOI:
http://dx.doi.org/10.1090/S0002993907090697
PII:
S 00029939(07)090697
Keywords:
Billingsley's dimension,
packing dimension,
Hausdorff dimension
Received by editor(s):
May 4, 2006
Received by editor(s) in revised form:
December 18, 2006
Published electronically:
October 18, 2007
Communicated by:
Jane M. Hawkins
Article copyright:
© Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
