Sum of two rare sets in a category base can be absolutely non-baire

TL;DR

This paper extends a result about the non-measurability of sums of special measure-zero sets to a broader context within category bases, highlighting the complexity of such sums.

Contribution

It generalizes existing measure-theoretic results to category bases, demonstrating absolute non-Baire properties of Minkowski sums of certain sets.

Findings

Minkowski sum of two rare sets can be absolutely non-Baire

Generalization of measure-zero set results to category bases

Extends classical results to a broader mathematical framework

Abstract

In this paper, we give generalized version in category bases of a result of Kharazishvili dealing with absolute nonmeasurability of the Minkowski sum of certain universal measure zero sets which were based on an earlier result of Erdos, Kunen and Mauldin in the real line.