Local entropy and <em>L<sup>q</sup></em>-dimensions of measures in doubling metric spaces
Anttila, R. (2020-11-04)
Anttila, R.
California State University
04.11.2020
Anttila, R. (2020). Local Entropy and Lq-Dimensions of Measures in Doubling Metric Spaces. The PUMP Journal of Undergraduate Research, 3, 226-243. Retrieved from https://journals.calstate.edu/pump/article/view/2434
https://creativecommons.org/licenses/by-nc/4.0/
(c) 2020 Roope Anttila. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
https://creativecommons.org/licenses/by-nc/4.0/
(c) 2020 Roope Anttila. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
https://creativecommons.org/licenses/by-nc/4.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe2020120299149
https://urn.fi/URN:NBN:fi-fe2020120299149
Tiivistelmä
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.
Kokoelmat
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