Pointwise dimensions and Rényi dimensions
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- by Ryszard Rudnicki PDF
- Proc. Amer. Math. Soc. 130 (2002), 1981-1982 Request permission
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 $q<1$.References
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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
- Received by editor(s): January 15, 2001
- Published electronically: 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 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 1981-1982
- MSC (2000): Primary 28A80; Secondary 28A78
- DOI: https://doi.org/10.1090/S0002-9939-02-06519-X
- MathSciNet review: 1896030