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Izvestiya: Mathematics, 1999, Volume 63, Issue 5, Pages 881–921
DOI: https://doi.org/10.1070/im1999v063n05ABEH000265
(Mi im265)
 

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
References:
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
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 1999, Volume 63, Issue 5, Pages 37–82
DOI: https://doi.org/10.4213/im265
Bibliographic databases:
MSC: 28A25, 28C05
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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\by V.~K.~Zakharov, A.~V.~Mikhalev
\paper The problem of general Radon representation for an arbitrary Hausdorff space
\jour Izv. RAN. Ser. Mat.
\yr 1999
\vol 63
\issue 5
\pages 37--82
\mathnet{http://mi.mathnet.ru/im265}
\crossref{https://doi.org/10.4213/im265}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1727590}
\zmath{https://zbmath.org/?q=an:0967.28012}
\transl
\jour Izv. Math.
\yr 1999
\vol 63
\issue 5
\pages 881--921
\crossref{https://doi.org/10.1070/im1999v063n05ABEH000265}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000085381600002}
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  • https://www.mathnet.ru/eng/im265
  • https://doi.org/10.1070/im1999v063n05ABEH000265
  • https://www.mathnet.ru/eng/im/v63/i5/p37
    Cycle of papers
    This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:525
    Russian version PDF:222
    English version PDF:14
    References:84
    First page:3
     
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