ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 28, 46, 6 Mikhalev, Alexander V., Moscow State University, Russia; Zakharov, Valery K., St-Petersburg State University of Desigh and Technology, Russia. Solution of Riesz-Radon problem. After the fundamental articles of Riesz, Radon and Hausdorff in 1909–1914 the problem of general Radon representation became actual: for Hausdorff topological spaces find a class of linear functionals isomorphic to the space of integrally represented Radon measures. After fundamental results of Halmos, Hewitt, Edwards, Bourbaki, Prohorov, Topsoe, and Polard the important step was made in 1995–1997 by König (a bijective version for isotone and positively-linear functionals). The authors have got one of possible solutions of the general Radon representation. For this reason the family of metasemicontinuous functions with compact support and the class of thin functionals are under consideration. Bijective and isomorphic versions of a solution are given. To get an isomorphic version the family of Radon bimeasures is introduced.