On certain regularity properties of Haar-null sets

• Autorzy: Pandelis Dodos
• Języki publikacji: 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.

Kategorie tematyczne

• 28C10: Set functions and measures on topological groups or semigroups, Haar measures, invariant measures
• 43A05: Measures on groups and semigroups, etc.
• 28A05: Classes of sets (Borel fields, σ -rings, etc.), measurable sets, Suslin sets, analytic sets

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2004
• Tom: 181
• Numer: 2
• Strony: 97-109

Daty

wydano

2004

Twórcy

autor

Pandelis Dodos

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

Identyfikatory

DOI

10.4064/fm181-2-1