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Mat. Sb., 2016, Volume 207, Number 3, Pages 137–152 (Mi msb8492)  

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

Decomposition of dyadic measures and unions of closed $\mathscr{U}$-sets for series in a Haar system

M. G. Plotnikov, Yu. A. Plotnikova

Vologda State Academy of Milk Industry

Abstract: New properties of finitely additive set functions (quasi-measures) and Borel measures on dyadic product groups $\mathbb{G}^m$ are established. The results obtained are applied to the theory of series in Haar systems — for example, for a broad family of classes of multiple Haar series on $\mathbb{G}^m$, a countable union of closed uniqueness sets is shown to be a uniqueness set too.
Bibliography: 18 titles.

Keywords: dyadic product group, multiple Haar series, $\mathscr{U}$-set, quasi-measure, Borel measure.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00417
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
Vologda State Dairy Farming Academy by N.V.Vereshchagin ВГМХА-2014
The research of the first-named author was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 14-01-00417) and the Programme of the President of the Russian Federation for the Support of Leading Scientific Schools (grant no. НШ-3682.2014.1). The research of the second-named author was carried out with the financial support of Vologda State Academy of Milk Industry (year 2014).

Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm8492

Full text: PDF file (578 kB)
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English version:
Sbornik: Mathematics, 2016, 207:3, 444–457

Bibliographic databases:

UDC: 517.518.113+517.518.117+517.518.36
MSC: Primary 42C25; Secondary 42A20, 42C05, 43A17
Received: 21.02.2015 and 04.07.2015

Citation: M. G. Plotnikov, Yu. A. Plotnikova, “Decomposition of dyadic measures and unions of closed $\mathscr{U}$-sets for series in a Haar system”, Mat. Sb., 207:3 (2016), 137–152; Sb. Math., 207:3 (2016), 444–457

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. G. G. Gevorkyan, “On uniqueness of series by Haar system”, J. Contemp. Math. Anal., 53:3 (2018), 128–133  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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