Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Billingsley's packing dimension

Author: Manav Das
Journal: Proc. Amer. Math. Soc. 136 (2008), 273-278
MSC (2000): Primary 28A78, 28A80
Published electronically: October 18, 2007
MathSciNet review: 2350413
Full-text PDF Free Access

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 $ \nu$, $ \gamma$, corresponding to the same stochastic process, if

$\displaystyle 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

$\displaystyle {\rm {Dim}}_{\nu}(F) = \theta ~{\rm {Dim}}_{\gamma}(F). $

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 28A78, 28A80

Retrieve articles in all journals with MSC (2000): 28A78, 28A80

Additional Information

Manav Das
Affiliation: Department of Mathematics, 328 Natural Sciences Building, University of Louisville, Louisville, Kentucky 40292

PII: S 0002-9939(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.

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia