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

### Local entropy and Lq-dimensions of measures in doubling metric spaces

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Author: Anttila, R.1
Organizations: 1University of Oulu, Pentti Kaiteran katu 1 Oulu, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 0.3 MB)
Language: English
Published: California State University, 2020
Publish Date: 2020-12-02
Description:

# 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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Series: PUMP. Journal of undergraduate research
ISSN: 2765-8724
ISSN-E: 2576-3725
ISSN-L: 2765-8724
Volume: 3
Pages: 226 - 243
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
Subjects: