Sets of uniqueness in compact, 0-dimensional metric groups

Abstract

An investigation is made of sets of uniqueness in a compact 0 0 -dimensional space. Such sets are defined by pointwise convergence of sequences of functions that generalize partial sums of trigonometric series on Vilenkin groups. Several analogs of classical uniqueness theorems are proved, including a version of N. Bary’s theorem on countable unions of closed sets of uniqueness.