This article is cited in 12 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.

UDC: 517.987

MSC: Primary 28C15; Secondary 28C05

Received: 27.04.2012 and 06.12.2012

DOI: 10.4213/sm8138

 English version: Sbornik: Mathematics, 2013, 204:5, 726–761

Bibliographic databases:

• 
• 
• 
• 
• 
• 
•