We show that in every Polish, abelian, non-locally compact group G there exist non-Haar null sets A and B such that the set {g ∈ G; (g+A) ∩ B is non-Haar null} is empty. This answers a question posed by Christensen.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-1, author = {Eva Matou\v skov\'a and Miroslav Zelen\'y}, title = {A note on intersections of non-Haar null sets}, journal = {Colloquium Mathematicae}, volume = {96}, year = {2003}, pages = {1-4}, zbl = {1031.28005}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-1} }
Eva Matoušková; Miroslav Zelený. A note on intersections of non-Haar null sets. Colloquium Mathematicae, Tome 96 (2003) pp. 1-4. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-1/