On certain regularity properties of Haar-null sets

Dodos, P

dc.contributor.author	Dodos, P	en
dc.date.accessioned	2014-03-01T01:21:09Z
dc.date.available	2014-03-01T01:21:09Z
dc.date.issued	2004	en
dc.identifier.issn	0016-2736	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/16097
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-3042853624&partnerID=40&md5=bad8b18907008d4481562164f7d4ba51	en
dc.subject.classification	Mathematics	en
dc.title	On certain regularity properties of Haar-null sets	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	Let X be an abelian Polish group. For every analytic Haar-null set A subset of or equal to 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 Ga 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 Haas-null set. A, there exists a. Borel Haar-null set B superset of or equal to 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.	en
heal.publisher	POLISH ACAD SCIENCES INST MATHEMATICS	en
heal.journalName	Fundamenta Mathematicae	en
dc.identifier.isi	ISI:000226352000001	en
dc.identifier.volume	181	en
dc.identifier.issue	2	en
dc.identifier.spage	97	en
dc.identifier.epage	109	en