Baklanov, A. ORCID: https://orcid.org/0000000315993618 (2016). On density properties of weakly absolutely continuous measures. Modern Problems in Mathematics and its Applications 1662 6272.

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Abstract
It is shown that some set of all step functions (and the set of all uniform limits of ones) allows an embedding into some compact subset (with respect to weakstar topology) of the set of all finitely additive measures of bounded variation in the form of an everywhere dense subset. Precisely, we considered the set of all step functions (the set of all uniform limits of such functions) such that integral of absolute value of the functions with respect to nonnegative finitely additive measure λ is equal to the unit. For these sets, the possibility of the embedding is proved for the cases of nonatomic and finite range measure λ; in the cases the compacts do not coincide. Namely, in the nonatomic measure case, it is shown that the mentioned sets of functions allow the embedding into the unit ball (in the strong normvariation) of weakly absolutely continuous measures with respect to λ in the form of a everywhere dense subset. In the finite range measure case, it is shown that the mentioned sets of functions allow the embedding into the unit sphere of weakly absolutely continuous measures with respect to λ in the form of a everywhere dense subset. In the last case the sphere is closed in the weakstar topology. An interpretation of these results is given in terms of an approach connected with an extension of linear control problems in the class of finitely additive measures.
Item Type:  Article 

Uncontrolled Keywords:  Finitely additive measures; Nonatomic or atomless measures; Weak absolute continuity; Weakstar topology 
Research Programs:  Advanced Systems Analysis (ASA) 
Depositing User:  Luke Kirwan 
Date Deposited:  26 Sep 2016 06:50 
Last Modified:  27 Aug 2021 17:27 
URI:  http://pure.iiasa.ac.at/13832 
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