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Measures in locally compact groups are carried by meager sets

Zakrzewski P., Zindulka O.

Journal of Applied Analysis

2001

Vol. 7, nr 2

225-233

We show that for a σ-finite diffused Borel measure in a nondiscrete locally bounded topological group there is a meager set whose complement is of measure zero.

Killing residual measures

Zindulka O.

Journal of Applied Analysis

1999

Vol. 5, nr 2

223-238

A σ-finite Borel measure in a topological space is called residual if each nowhere dense set has measure zero. We show that in various types of spaces without isolated points there are no residual measures. Among these spaces are e.g. σ-spaces, locally metrizable spaces, locally separable spaces, spaces that have a σ-point-finite π -base, submanifolds.

Descriptive properties of spaces of measures

Holicky P., Kalenda O.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 1

37-51

The spaces of Borel probabilities on a topological space X inherit a number of topological properties of X. We show in particular that the space of tight probabilities on a Cech-analytic space is Cech-analytic. Analogical results are shown for several other classes of generalized analytic and complete topological spaces.