A dimension result arising from

the -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

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Abstract | References | Similar Articles | Additional Information

Abstract: We give a rigorous proof of the following heuristic result: Let be a Borel probability measure and let be the -spectrum of . If is differentiable at , then the Hausdorff dimension and the entropy dimension of equal . 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.

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Additional Information

**Sze-Man Ngai**

Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong

Email:
smngai@math.cuhk.edu.hk

DOI:
https://doi.org/10.1090/S0002-9939-97-03974-9

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