In the context of arbitrary Polish groups, we investigate the Galvin–Mycielski–Solovay characterization of strong measure zero sets as those sets for which a meager collection of right translates cannot cover the whole group.
"Strong measure zero sets in Polish groups." Illinois J. Math. 60 (3-4) 751 - 760, Fall and Winter 2016. https://doi.org/10.1215/ijm/1506067289