MEASURE ZERO SETS WHOSE ALGEBRAIC SUM IS NON-MEASURABLE
MEASURE ZERO SETS WHOSE ALGEBRAIC SUM IS NON-MEASURABLE
In this note we will show that for every natural number $n>0$ there exists an $S\subset[0,1]$ such that its $n$-th algebraic sum $nS=S+\cdots +S$ is a nowhere dense measure zero set, but its $n+1$-st algebraic sum $nS+S$ is neither measurable nor it has the Baire property. In addition, the set …