On certain regularity properties of Haar-null sets

Pandelis Dodos. "On certain regularity properties of Haar-null sets." Fundamenta Mathematicae 181.2 (2004): 97-109. <http://eudml.org/doc/282939>.

@article{PandelisDodos2004,
abstract = {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.},
author = {Pandelis Dodos},
journal = {Fundamenta Mathematicae},
keywords = {analytic Haar-null set; Borel Haar-null set; co-analytic sets},
language = {eng},
number = {2},
pages = {97-109},
title = {On certain regularity properties of Haar-null sets},
url = {http://eudml.org/doc/282939},
volume = {181},
year = {2004},
}

TY - JOUR
AU - Pandelis Dodos
TI - On certain regularity properties of Haar-null sets
JO - Fundamenta Mathematicae
PY - 2004
VL - 181
IS - 2
SP - 97
EP - 109
AB - 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.
LA - eng
KW - analytic Haar-null set; Borel Haar-null set; co-analytic sets
UR - http://eudml.org/doc/282939
ER -