FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 1, PAGES 33-46
V. K. Zakharov
A. V. Mikhalev
Abstract
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After the fundamental papers of Riesz, Radon and Hausdorff in
1909--1914 the \emph{problem of general Radonean representation}
became actual: \emph{find for Hausdorff topological spaces
a class of linear functionals isomorphically integrally representable
by all Radon measures}. In 1952--1953 the bijective solution of
the problem of Radonean representation for locally compact spaces
was obtained by Halmos, Hewitt, Edwards, etc.
For bounded Radon measures
on a Tychonoff space the problem of isomorphic
Radonean representation was solved
in 1956 by Yu. V. Prokhorov.
In 1996--1997 the authors obtained one of possible solutions
of the problem of general Radonean representation using the family
of \emph{metasemicontinuous functions with compact supports} and
the class of \emph{thin functionals} on it.
After this the \emph{question if the theorem about general Radonean
representation covers the Riesz--Radon theorem} was still left open. In this
paper the positive answer to this question is given.
All articles are published in Russian.
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Last modified: May 10, 2001