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

Authors

  • 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.

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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

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The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.