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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 6, Pages 1343–1358
DOI: https://doi.org/10.33048/smzh.2020.61.608
(Mi smj6054)
 

This article is cited in 1 scientific paper (total in 1 paper)

On uniform distributions on metric compacta

A. V. Ivanov

Institute of Applied Mathematical Research of the Karelian Research Centre RAS, Petrozavodsk
Full-text PDF (520 kB) Citations (1)
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Abstract: We introduce the notion of uniform distribution on a metric compactum. The desired distribution is defined as the limit of a sequence of the classical uniform distributions on finite sets which are uniformly distributed on the compactum in the geometric sense. We show that a uniform distribution exists on the metrically homogeneous compacta and the canonically closed subsets of a Euclidean space whose boundary has Lebesgue measure zero. If a compactum (satisfying some metric constraints) admits a uniform distribution then so does its every canonically closed subset that has zero uniform measure of the boundary. We prove that compacta, admitting a uniform distribution, are dimensionally homogeneous in the sense of box-dimension.
Keywords: uniform distribution, Kantorovich–Rubinshtein metric, box-dimension, space of probability measures.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation
The study was carried out under the State Task to the Institute of Applied Mathematical Research of the Karelian Scientific Center of the Russian Academy of Sciences.
Received: 09.01.2020
Revised: 05.08.2020
Accepted: 10.08.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 6, Pages 1075–1086
DOI: https://doi.org/10.1134/S0037446620060087
Bibliographic databases:
Document Type: Article
UDC: 515.12+519.21
MSC: 35R30
Language: Russian
Citation: A. V. Ivanov, “On uniform distributions on metric compacta”, Sibirsk. Mat. Zh., 61:6 (2020), 1343–1358; Siberian Math. J., 61:6 (2020), 1075–1086
Citation in format AMSBIB
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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