Local Entropy and Lq-Dimensions of Measures in Doubling Metric Spaces

  • Roope Anttila University of Oulu
DOI: https://doi.org/10.46787/pump.v3i0.2434
Keywords: multifractal analysis; local Lq-dimension; local entropy dimension

Abstract

We define restricted entropy and Lq-dimensions of measures in doubling metric spaces and show that these definitions are consistent with the monotonicity of Lq-dimensions. This provides a correct proof for a theorem considering the relationships between local entropy and Lq-dimensions in a paper by Käenmäki, Rajala and Suomala, the original proof of which makes use of a slightly erroneous proposition.

Published
2020-11-04
How to Cite
Anttila, R. (2020). Local Entropy and Lq-Dimensions of Measures in Doubling Metric Spaces. The PUMP Journal of Undergraduate Research, 3, 226-243. https://doi.org/10.46787/pump.v3i0.2434
Issue
Vol. 3 (2020): PUMP Journal of Undergraduate Research
Section
Articles

Copyright (c) 2020 Roope Anttila

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