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On weakly measurable functions

Żeberski S.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 4

421-428

We show that if T is an uncountable Polish space, X is a metrizable space and f : T → X is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f [T ∖ M] is a separable space. We also give an example showing that “metrizable” cannot be replaced by “normal”.

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.