Two rare sets in a category base with an absolutely non-Baire sum

Abstract In this paper, we give generalized versions (in category bases) of two results of Kharazishvili, the second one dealing with absolute nonmeasurability of Minkowski’s sum of two universal measure zero sets with respect to the completion of any non-zero, σ {{\sigma}} -finite, Borel measure. Both results were based on an earlier result of Erdös, Kunen and Mauldin.