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.**Patrick Billingsley,*Hausdorff dimension in probability theory*, Illinois J. Math.**4**(1960), 187–209. MR**0131903****2.**Patrick Billingsley,*Hausdorff dimension in probability theory. II*, Illinois J. Math.**5**(1961), 291–298. MR**0120339****3.**Helmut Cajar,*Billingsley dimension in probability spaces*, Lecture Notes in Mathematics, vol. 892, Springer-Verlag, Berlin-New York, 1981. MR**654147****4.**C. D. Cutler,*A note on equivalent interval covering systems for Hausdorff dimension on 𝑅*, Internat. J. Math. Math. Sci.**11**(1988), no. 4, 643–649. MR**959443**, https://doi.org/10.1155/S016117128800078X**5.**Chao Shou Dai and S. James Taylor,*Defining fractals in a probability space*, Illinois J. Math.**38**(1994), no. 3, 480–500. MR**1269700****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**(2005), no. 11, 4249–4268. MR**2156710**, https://doi.org/10.1090/S0002-9947-05-04031-6**9.**Gerald A. Edgar,*Measure, topology, and fractal geometry*, Undergraduate Texts in Mathematics, Springer-Verlag, New York, 1990. MR**1065392****10.**S. James Taylor,*The measure theory of random fractals*, Math. Proc. Cambridge Philos. Soc.**100**(1986), no. 3, 383–406. MR**857718**, https://doi.org/10.1017/S0305004100066160

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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.