Geodesic
Proper Quasi-Measure Criterion
Matematičeskie zametki, Tome 81 (2007) no. 5, pp. 751-759

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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. 
@article{MZM_2007_81_5_a12,
     author = {M. G. Svistula},
     title = {Proper {Quasi-Measure} {Criterion}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {751--759},
     publisher = {mathdoc},
     volume = {81},
     number = {5},
     year = {2007},
     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/