On a density property of weakly absolutely continuous measures. General case

15046 10 80360 2 221961 document 80360 50-01.pdf application/pdf bb60609c7ebc98c7dd3b931a70d35cf4 MD5 268596 2018-01-12 09:14:00 https://pure.iiasa.ac.at/id/eprint/15046/1/50-01.pdf 15046 1 1 application/pdf text en public cc_by

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published 80361 2 221970 document 80361 lightbox.jpg image/png 8d49000f3f93780f23a171b0d6b79781 MD5 42674 2018-01-12 09:24:09 https://pure.iiasa.ac.at/id/eprint/15046/2/lightbox.jpg 15046 2 2 image/png other Thumbnails conversion from text to thumbnail_lightbox en public

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/80360 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/80360 http://eprints.org/relation/isIndexCodesVersionOf https://pure.iiasa.ac.at/id/document/80360 archive 353 disk0/00/01/50/46 2018-01-12 09:17:08 2021-08-27 17:29:47 2018-01-12 09:17:08 article show Baklanov A. 2067 0000-0003-1599-3618 On a density property of weakly absolutely continuous measures. General case pub prog_asa finitely additive measures, weak absolute continuity, weak-star topology, nonatomic or atomless measures, Sobczyk-Hammer decomposition It is shown that some set of all step functions (and the set of all uniform limits of such functions) allows an embedding into a compact subset (with respect to weak-star topology) of the set of all finitely additive measures of bounded variation in the form of an everywhere dense subset. In particular, we consider the set of all step functions (the set of all uniform limits of such functions) such that an integral of absolute value of the functions with respect to nonnegative finitely additive measure λ is equal to unity. For these sets, the possibility of embedding is proved without any additional assumptions on λ; this generalizes the previous results. Using the Sobczyk-Hammer decomposition theorem, we show that for λ with the finite range, the above-mentioned sets of functions allow an embedding into the unit sphere (in the strong norm-variation) of weakly absolutely continuous measures with respect to λ in the form of an everywhere dense subset. For λ with an infinite range, the above-mentioned sets of functions allow an embedding into the unit ball of weakly absolutely continuous measures with respect to λ in the form of an everywhere dense subset. The results can be helpful for an extension of linear impulse control problems in the class of finitely additive measures to obtain robust representations of reachable sets given by constraints of asymptotic character. 2017-10-28 published Udmurtskogo Gosudarstvennogo Universiteta http://imi.udsu.ru/doc/issues/50-01.pdf 22 public Izvestiya Instituta Matematiki i Informatiki 2 50 3-12 TRUE 2410-1737 FALSE no info:eu-repo/semantics/article