Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A dimension result arising from the $L^q$-spectrum of a measure

Author: Sze-Man Ngai
Journal: Proc. Amer. Math. Soc. 125 (1997), 2943-2951
MSC (1991): Primary 28A80; Secondary 28A78
MathSciNet review: 1402878
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a rigorous proof of the following heuristic result: Let $\mu$ be a Borel probability measure and let $\tau (q)$ be the $L^{q}$-spectrum of $\mu$. If $\tau (q)$ is differentiable at $q=1$, then the Hausdorff dimension and the entropy dimension of $\mu$ equal $\tau ’(1)$. Our result improves significantly some recent results of a similar nature; it is also of particular interest for computing the Hausdorff and entropy dimensions of the class of self-similar measures defined by maps which do not satisfy the open set condition.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 28A80, 28A78

Retrieve articles in all journals with MSC (1991): 28A80, 28A78

Additional Information

Sze-Man Ngai
Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong

Keywords: Entropy dimension, Hausdorff dimension, $L^{q}$-spectrum
Received by editor(s): February 28, 1996
Received by editor(s) in revised form: May 7, 1996
Additional Notes: Research supported by a postdoctoral fellowship of the Chinese University of Hong Kong.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society