Geodesic
Proper Quasi-Measure Criterion
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 751-759 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the well-known theorem about the decomposition of a quasi-measure into the sum of a measure and a proper quasi-measure, we give a new representation of the measure summand, which allows us to derive a proper quasi-measure test. We use this test to solve the problem of the sum of proper quasi-measures and generalize the results obtained to the case of quasi-states.
Keywords: measure, quasi-measure, decomposition theorem, proper measure, regular Borel measure, positive linear functional, quasi-state. 
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     author = {M. G. Svistula},
     title = {Proper {Quasi-Measure} {Criterion}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a12/}
}
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M. G. Svistula. Proper Quasi-Measure Criterion. Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 751-759. http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a12/

[1] J. F. Aarnes, “Quasi-states and quasi-measures”, Adv. Math., 86:1 (1991), 41–67 | DOI | MR | Zbl

[2] P. Khalmosh, Teoriya mery, IL, M., 1953 | MR | Zbl

[3] J. F. Aarnes, “Construction of non-subadditive measures and discretization of Borel measures”, Fund. Math., 147:3 (1995), 213–237 | MR | Zbl

[4] R. F. Wheeler, “Quasi-measures and dimension theory”, Topology Appl., 66:1 (1995), 75–92 | DOI | MR | Zbl

[5] D. J. Grubb, T. LaBerge, “Additivity of quasi-measures”, Proc. Amer. Math. Soc., 126:10 (1998), 3007–3012 | DOI | MR | Zbl

[6] T. LaBerge, “Supports of quasi-measures”, Houston J. Math., 24:2 (1998), 301–312 | MR | Zbl