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

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.