FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 1, PAGES 33-46

**Connections between the integral Radonean representations for
locally compact and Hausdorff spaces**

V. K. Zakharov

A. V. Mikhalev

Abstract

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After the fundamental papers of Riesz, Radon and Hausdorff in
1909--1914 the *problem of general Radonean representation*
became actual: *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 *metasemicontinuous functions with compact
supports* and the class of *thin functionals* on it.

After this the *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.

Location: http://mech.math.msu.su/~fpm/eng/k01/k011/k01103h.htm

Last modified: May 10, 2001