Billingsley's packing dimension

Author:
Manav Das

Journal:
Proc. Amer. Math. Soc. **136** (2008), 273-278

MSC (2000):
Primary 28A78, 28A80

DOI:
https://doi.org/10.1090/S0002-9939-07-09069-7

Published electronically:
October 18, 2007

MathSciNet review:
2350413

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Abstract | References | Similar Articles | Additional Information

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

**1.**P. Billingsley,*Hausdorff Dimension in Probability Theory I*, Ill. J. Math., 4, 1960, pp. 187-209. MR**0131903 (24:A1750)****2.**P. Billingsley,*Hausdorff Dimension in Probability Theory II*, Ill. J. Math., 5, 1961, pp. 291-298. MR**0120339 (22:11094)****3.**Helmut Cajar,*Billingsley dimension in probability spaces*, Lecture Notes in Mathematics, 892, Springer-Verlag, Berlin-New York, 1981. MR**654147 (84a:10055)****4.**C. D. Cutler,*A note on equivalent interval covering systems for Hausdorff dimension on*, Int. J. Math. Math. Sci., 11, no. 4, 1988, pp. 643-650. MR**959443 (89h:28008)****5.**Chao Shou Dai and S. James Taylor,*Defining fractals in a probability space,*Illinois J. Math., 38, no. 3, 1994, pp. 480-500. MR**1269700 (95f:28011)****6.**Manabendra Das,*Pointwise Local Dimensions*, Ph. D. Thesis, The Ohio State University, 1996.**7.**Manav Das,*Packing Measures, Dimensions and Mutual Singularity*, preprint.**8.**Manav Das,*Hausdorff Measures, Dimensions and Mutual Singularity*, Trans. Amer. Math. Soc, 357, no. 11, 2005, pp. 4249-4268 MR**2156710 (2006g:28010)****9.**G. A. Edgar,*Measure, topology, and fractal geometry,*Springer-Verlag, New York, 1990. MR**1065392 (92a:54001)****10.**S. James Taylor,*The measure theory of random fractals*, Math. Proc. Cambridge Philos. Soc., 100, no. 3, 1986, pp. 383-406. 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:
https://doi.org/10.1090/S0002-9939-07-09069-7

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.