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Pointwise dimensions and Rényi dimensions

Author(s): Ryszard Rudnicki
Journal: Proc. Amer. Math. Soc. 130 (2002), 1981-1982.
MSC (2000): Primary 28A80; Secondary 28A78
Posted: January 25, 2002
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Abstract: We prove that the local lower and upper pointwise dimensions of a probability measure $\mu$ are bounded from below by the lower generalized dimension ${\underline D}_{\mu}(q)$ for $q>1$and from above by the upper generalized dimension ${\overline D}_{\mu}(q)$ for $q<1$.

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Additional Information:

Ryszard Rudnicki
Affiliation: Institute of Mathematics, Polish Academy of Sciences and Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland
Email: rudnicki@us.edu.pl

DOI: 10.1090/S0002-9939-02-06519-X
PII: S 0002-9939(02)06519-X
Keywords: Pointwise dimension, generalized (R\'enyi) dimension, measure
Received by editor(s): January 15, 2001
Posted: January 25, 2002
Additional Notes: This research was partially supported by the State Committee for Scientific Research (Poland) Grant No. 2 P03A 010 161.
Communicated by: David Preiss
Copyright of article: Copyright 2002, American Mathematical Society

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