RMC - Vol. 2, supplementary - J. L. de María/B. Rodríguez-Salinas

Full paper in PDF:
$% J. L. de María and B. Rodríguez-Salinas, Structure of measures on topological spaces, Rev. Mat. Univ. Complut. Madrid 2 (1989), supplementary, 103–118.%$

Structure of Measures on Topological Spaces

José L. DE MARíA and Baltasar RODRíGUEZ-SALINAS

Departamento de Matemáticas Fundamentales U.N.E.D. Ciudad Universitaria 28040 Madrid — Spain	Departamento de Ánálisis Matemático Facultad de Matemáticas Universidad Complutense de Madrid 28040 Madrid — Spain

ABSTRACT

The Radon spaces of type ( $T$ ), i.e., topological spaces for which every finite Borel measure on $_O_$ is $t$ -additive and $T$ -regular are characterized. The class of these spaces is very wide and in particular it contains the Radon spaces. We extend the results of Marczewski an Sikorski to the $s$ -metrizable spaces and to the subsets of the Banach spaces endowed with the weak topology. Finally, the completely additive families of measurable subsets related with the works of Hansell, Koumoullis, and Fremlin are studied.

1980 Mathematics Subject Classification (1985 revision): 28C15, 46G12