| Autor: |
Ovadia, S Ben, Rodriguez-Hertz, F |
| Předmět: |
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| Zdroj: |
IMRN: International Mathematics Research Notices; Jun2024, Vol. 2024 Issue 11, p9469-9481, 13p |
| Abstrakt: |
We introduce a notion of a point-wise entropy of measures (i.e. local entropy) called neutralized local entropy , and compare it with the Brin-Katok local entropy. We show that the neutralized local entropy coincides with Brin-Katok local entropy almost everywhere. Neutralized local entropy is computed by measuring open sets with a relatively simple geometric description. Our proof uses a measure density lemma for Bowen balls, and a version of a Besicovitch covering lemma for Bowen balls. As an application, we prove a lower point-wise dimension bound for invariant measures, complementing the previously established bounds for upper point-wise dimension. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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