Geodesic
Deficient topological measures and functionals generated by them
Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 726-761

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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. 
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     author = {M. G. Svistula},
     title = {Deficient topological measures and functionals generated by them},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2013_204_5_a4/}
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M. G. Svistula. Deficient topological measures and functionals generated by them. Sbornik. Mathematics, Tome 204 (2013) no. 5, pp. 726-761. http://geodesic.mathdoc.fr/item/SM_2013_204_5_a4/