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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 6, Pages 3–18 (Mi izv407)  

This article is cited in 7 scientific papers (total in 7 papers)

The problem of general Radon representation for an arbitrary Hausdorff space. II

V. K. Zakharov, A. V. Mikhalev

Centre for New Information Technologies, Moscow State University

Abstract: The problem of general Radon representation is as follows. Given a Hausdorff topological space, find the space of linear functionals that are representable as integrals over all Radon measures. One of the possible solutions of this problem was obtained in Part I of this paper (see [39]). In Part II we establish that the classical theorems of Riesz–Radon and Prokhorov are corollaries of the theorem on general integral Radon representation proved in [39].

DOI: https://doi.org/10.4213/im407

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English version:
Izvestiya: Mathematics, 2002, 66:6, 1087–1101

Bibliographic databases:

UDC: 517.981.1+517.518.1+517.982.3
MSC: 28A25, 28C05
Received: 02.07.2001

Citation: V. K. Zakharov, A. V. Mikhalev, “The problem of general Radon representation for an arbitrary Hausdorff space. II”, Izv. RAN. Ser. Mat., 66:6 (2002), 3–18; Izv. Math., 66:6 (2002), 1087–1101

Citation in format AMSBIB
\Bibitem{ZakMik02}
\by V.~K.~Zakharov, A.~V.~Mikhalev
\paper The problem of general Radon representation for an arbitrary Hausdorff space.~II
\jour Izv. RAN. Ser. Mat.
\yr 2002
\vol 66
\issue 6
\pages 3--18
\mathnet{http://mi.mathnet.ru/izv407}
\crossref{https://doi.org/10.4213/im407}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1970350}
\zmath{https://zbmath.org/?q=an:1092.28009}
\transl
\jour Izv. Math.
\yr 2002
\vol 66
\issue 6
\pages 1087--1101
\crossref{https://doi.org/10.1070/IM2002v066n06ABEH000407}


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    This publication is cited in the following articles:
    1. V. K. Zakharov, “The Riesz–Radon Problem of Characterizing Integrals and the Weak Compactness of Radon Measures”, Proc. Steklov Inst. Math., 248 (2005), 101–110  mathnet  mathscinet  zmath
    2. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “The Riesz–Radon–Fréchet problem of characterization of integrals”, Russian Math. Surveys, 65:4 (2010), 741–765  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Characterization of Radon integrals as linear functionals”, J. Math. Sci., 185:2 (2012), 233–281  mathnet  crossref  mathscinet
    4. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “The characterization of integrals with respect to arbitrary Radon measures by the boundedness indices”, J. Math. Sci., 185:3 (2012), 417–429  mathnet  crossref
    5. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Descriptive spaces and proper classes of functions”, J. Math. Sci., 213:2 (2016), 163–200  mathnet  crossref  mathscinet
    6. V. K. Zakharov, A. V. Mikhalev, T. V. Rodionov, “Postclassical families of functions proper for descriptive and prescriptive spaces”, J. Math. Sci., 221:3 (2017), 360–383  mathnet  crossref  mathscinet
    7. Machsoudi S., Rejali A., “on the Dual of Certain Locally Convex Function Spaces”, Bull. Iran Math. Soc., 41:4 (2015), 1003–1017  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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