Theoretical analysis demonstrates the absolute nonmeasurability of Minkowski sums in category bases, extending classical results on rare sets.
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 {{σ}} -finite, Borel measure. Both results were based on an earlier result of Erdös, Kunen and Mauldin.
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Basu et al. (2026) studied this question.
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