Deficient topological measures and functionals generated by them

Journal Article · Fri May 31 00:00:00 EDT 2013 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2013V204N05ABEH004318· OSTI ID:22122878

Svistula, Marina G ^[1]

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1. Samara State University, Samara (Russian Federation)

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.

• OSTI ID: 22122878
• Journal Information: Sbornik. Mathematics, Vol. 204, Issue 5; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
FUNCTIONALS
INTEGRALS
SET THEORY
TOPOLOGY