Strongly meager sets do not form an ideal (Q2732506)

A~set \(X\subseteq\mathbb R\) is strongly meager if for every measure zero set~\(H\), \(\{x+y:x\in X\), \(y\in H\}\neq\mathbb R\). This definition is the category analogue of a~characterization of the notion of strongly measure zero sets. The strongly measure zero sets form a~\(\sigma\)-ideal. However, the authors prove, under the continuum hypothesis, that the collection of strongly meager sets is not an ideal.