Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J. F. Aarnes, “Quasi-states and quasi-measures,” Adv. Math. 86(1), 41–67 (1991).
P. Halmos, Measure Theory (Van Nostrand, New York, 1950; Inostr. Lit., Moscow, 1953).
J. F. Aarnes, “Construction of non-subadditive measures and discretization of Borel measures,” Fund. Math. 147(3), 213–237 (1995).
R. F. Wheeler, “Quasi-measures and dimension theory,” Topology Appl. 66(1), 75–92 (1995).
D. J. Grubb and T. LaBerge, “Additivity of quasi-measures,” Proc. Amer. Math. Soc. 126(10), 3007–3012 (1998).
T. LaBerge, “Supports of quasi-measures,” Houston J. Math. 24(2), 301–312 (1998).
Author information
Authors and Affiliations
Additional information
Original Russian Text © M. G. Svistula, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 5, pp. 751–759.
Rights and permissions
About this article
Cite this article
Svistula, M.G. Proper quasi-measure criterion. Math Notes 81, 671–680 (2007). https://doi.org/10.1134/S0001434607050136
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1134/S0001434607050136