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Mat. Sb., 2013, Volume 204, Number 5, Pages 109–142 (Mi msb8138)  

This article is cited in 4 scientific papers (total in 4 papers)

Deficient topological measures and functionals generated by them

M. G. Svistula

Samara State University

Abstract: This paper looks at the properties of deficient topological measures, which are a generalization of topological measures. Integration of a real function that is continuous on a compact set with respect to a deficient topological measure is also investigated. The notions of $r$- and $l$-functionals are introduced and an analogue of the Riesz representation theorem is obtained for them. As corollaries, both well-known and new results for quasi-integrals and topological measures are presented (for example, a new version of the definition of a quasi-integral).
Bibliography: 16 titles.

Keywords: deficient topological measure, topological measure, $r$- and $l$-functionals, quasi-integral, Riesz representation theorem.

DOI: https://doi.org/10.4213/sm8138

Full text: PDF file (761 kB)
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English version:
Sbornik: Mathematics, 2013, 204:5, 726–761

Bibliographic databases:

UDC: 517.987
MSC: Primary 28C15; Secondary 28C05
Received: 27.04.2012 and 06.12.2012

Citation: M. G. Svistula, “Deficient topological measures and functionals generated by them”, Mat. Sb., 204:5 (2013), 109–142; Sb. Math., 204:5 (2013), 726–761

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8138
  • http://mi.mathnet.ru/eng/msb/v204/i5/p109

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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. M. Svistula, “On integration with respect to a DT-measure”, Positivity, 20:3 (2016), 579–598  crossref  mathscinet  zmath  isi  scopus
    2. M. Svistula, “Decomposition of transformations”, Acta Math. Hung., 155:2 (2018), 376–392  crossref  mathscinet  zmath  isi  scopus
    3. S. V. Butler, “Ways of obtaining topological measures on locally compact spaces”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 25 (2018), 33–45  mathnet  crossref
    4. Butler S.V., “Signed Topological Measures on Locally Compact Spaces”, Anal. Math., 45:4 (2019), 757–773  crossref  mathscinet  zmath  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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