On sets which can be moved away from sets of a certain family

Abstract An operation which assigns to an arbitrary family of sets the class of sets which can be translated away from every set from the fixed family is considered in abelian groups. Assuming CH it is proven that on the real line meager sets can be defined as sets “shiftable” from the family of strong measure zero sets ( K = SMZ ⁎ ) . A similar result is shown for Lebesgue null sets and strongly meager sets ( N = SM ⁎ ) . Additionally a certain characterization of the family of meager-additive sets is given.