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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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/
@article{MZM_2007_81_5_a12,
     author = {M. G. Svistula},
     title = {Proper {Quasi-Measure} {Criterion}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {751--759},
     year = {2007},
     volume = {81},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a12/}
}
TY  - JOUR
AU  - M. G. Svistula
TI  - Proper Quasi-Measure Criterion
JO  - Matematičeskie zametki
PY  - 2007
SP  - 751
EP  - 759
VL  - 81
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a12/
LA  - ru
ID  - MZM_2007_81_5_a12
ER  - 
%0 Journal Article
%A M. G. Svistula
%T Proper Quasi-Measure Criterion
%J Matematičeskie zametki
%D 2007
%P 751-759
%V 81
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_5_a12/
%G ru
%F 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