On G-transitive version of perfectly meager sets

Abstract

We study the G-invariant version of perfectly meager sets (a generalization of the notion of AFC sets). We find the necessary and sufficient conditions for the inclusion AFC'G ⊆ I. In particular, we partially characterize for which groups G of automorphisms of the Cantor space every AFC'G set is Lebesgue null.

Keywords

• perfectly meager sets
• strongly meager sets
• afc' sets