RIEMANN–LEBESGUE PROPERTIES OF BANACH SPACES ASSOCIATED WITH SUBSETS OF COUNTABLE DISCRETE ABELIAN GROUPS

For a subset (Lambda) of the dual group of a compact metrizable abelian group, we introduce the type I-, II-, and III(Lambda)-Riemann–Lebesgue property of a Banach space. As an application we use these properties to characterize Rajchman sets.