THE ALGEBRAIC SUM OF A SET OF STRONG MEASURE ZERO AND A PERFECTLY MEAGER SET REVISITED

Abstract

We present simple proofs of the following theorems:
It is consistent with ZFC that there are a strongly measure zero set X, and a setY ∈ AFC such that X + Y contains a perfect set. It is consistent with ZFC that there are a set X of universal measure zero, and a strongly meager set Y such that X + Y contains a perfect set.