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• # Artykuł - szczegóły

## Fundamenta Mathematicae

2004 | 181 | 2 | 97-109

## On certain regularity properties of Haar-null sets

EN

### Abstrakty

EN
Let X be an abelian Polish group. For every analytic Haar-null set A ⊆ X let T(A) be the set of test measures of A. We show that T(A) is always dense and co-analytic in P(X). We prove that if A is compact then T(A) is $G_δ$ dense, while if A is non-meager then T(A) is meager. We also strengthen a result of Solecki and we show that for every analytic Haar-null set A, there exists a Borel Haar-null set B ⊇ A such that T(A)∖ T(B) is meager. Finally, under Martin's Axiom and the negation of Continuum Hypothesis, some results concerning co-analytic sets are derived.

97-109

wydano
2004

### Twórcy

autor
• Department of Mathematics, National Technical University of Athens, Zografou Campus, 157 80 Athens, Greece