Billingsley’s packing dimension
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- by Manav Das PDF
- Proc. Amer. Math. Soc. 136 (2008), 273-278 Request permission
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 $\nu$, $\gamma$, corresponding to the same stochastic process, if \[ F \subseteq \left \{ \omega \in \Omega : \lim _{n} \frac {\log \gamma (c_{n}(\omega ))}{\log \nu (c_{n}(\omega ))} = \theta \right \}, \] then we prove that \[ {\rm {Dim}}_{\nu }(F) = \theta ~{\rm {Dim}}_{\gamma }(F). \]References
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Additional Information
- Manav Das
- Affiliation: Department of Mathematics, 328 Natural Sciences Building, University of Louisville, Louisville, Kentucky 40292
- MR Author ID: 632693
- Email: manav@louisville.edu
- 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
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2350413