Union results for thin sets

Abstract

Let G be a compact abelian group and let Γ be its (discrete) dual group. Denote by M(G) the space of complex regular Borel measures on G.Let E be a subset of Γ. Then:(i) E is called a Rajchman set if, for all μ ∈M(G) implies (ii) E is called a set of continuity if given ε > 0 there exists δ > 0 such that if and(iii) E is called a parallelepiped of dimension N if |E| = 2N and there are two-element sets . (The multiplication indicated here is the group operation.)