Dichotomies of the set of test measures of a haar-null set

Dodos, P

dc.contributor.author	Dodos, P	en
dc.date.accessioned	2014-03-01T01:20:13Z
dc.date.available	2014-03-01T01:20:13Z
dc.date.issued	2004	en
dc.identifier.issn	0021-2172	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15862
dc.relation.uri	http://www.scopus.com/inward/record.url?eid=2-s2.0-14644399216&partnerID=40&md5=3841984f2822eb53498c7a21af0919a1	en
dc.subject.classification	Mathematics	en
dc.subject.other	SPACES	en
dc.subject.other	PROBABILITY	en
dc.subject.other	PREVALENCE	en
dc.title	Dichotomies of the set of test measures of a haar-null set	en
heal.type	journalArticle	en
heal.language	English	en
heal.publicationDate	2004	en
heal.abstract	We prove that if X is a Polish space and F a face of P(X) with the Baire property, then F is either a meager or a co-meager subset of P(X). As a consequence we show that for every abelian Polish group X and every analytic Haar-null set A subset of X, the set of test measures T(A) of A is either meager or co-meager. We characterize the non-locally-compact groups as the ones for which there exists a closed Haar-null set F subset of X with T(F) meager. Moreover, we answer negatively a question of J. Mycielski by showing that for every non-locally-compact abelian Polish group and every sigma-compact subgroup G of X there exists a G-invariant F-sigma subset of X which is neither prevalent nor Haar-null.	en
heal.publisher	MAGNES PRESS	en
heal.journalName	Israel Journal of Mathematics	en
dc.identifier.isi	ISI:000227601600002	en
dc.identifier.volume	144	en
dc.identifier.spage	15	en
dc.identifier.epage	28	en