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This article is cited in 10 scientific papers (total in 10 papers)
The problem of general Radon representation for an arbitrary Hausdorff space
V. K. Zakharova, A. V. Mikhalevb a St. Petersburg State University of Technology and Design
b M. V. Lomonosov Moscow State University
Abstract:
After the fundamental work of Riesz, Radon and Hausdorff in the period 1909–1914, the following problem of general Radon representation emerged: for any Hausdorff space find the space of linear functionals that are integrally representable by Radon measures. In the early 1950s, a partial solution of this problem (the bijective version) for locally compact spaces was obtained by Halmos, Hewitt, Edwards, Bourbaki and others. For bounded Radon measures on a Tychonoff space, the problem of isomorphic Radon representation was solved in 1956 by Prokhorov.
In this paper we give a possible solution of the problem of general Radon representation. To do this, we use the family of metasemicontinuous functions with compact support and the class of thin functionals. We present bijective and isomorphic versions of the solution (Theorems 1 and 2 of § 2.5). To get the isomorphic version, we introduce the family of Radon bimeasures.
Received: 19.12.1997
Citation:
V. K. Zakharov, A. V. Mikhalev, “The problem of general Radon representation for an arbitrary Hausdorff space”, Izv. RAN. Ser. Mat., 63:5 (1999), 37–82; Izv. Math., 63:5 (1999), 881–921
Linking options:
https://www.mathnet.ru/eng/im265https://doi.org/10.1070/im1999v063n05ABEH000265 https://www.mathnet.ru/eng/im/v63/i5/p37
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Abstract page: | 525 | Russian version PDF: | 222 | English version PDF: | 14 | References: | 84 | First page: | 3 |
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