Finite-power strong measure zero conjecture

Let $X$ be a set of reals. Say that $X$ has strong measure zero if, for every sequence of positive real numbers, there is a sequence of intervals of the corresponding lengths covering $X$. Let $\mathfrak{b}$ denote the bounding number.

Finite-power strong measure zero conjecture. If $X$ has strong measure zero and $|X|<\mathfrak{b}$, then all finite powers of $X$ have strong measure zero.

This conjecture was posed as the problem of Issue 7. The supplied text identifies it as solved, so it is recorded as a theorem rather than an open conjecture.