On $M_0$-sets for series with respect to characters of compact zero-dimensional groups

Abstract

Generalizing our previous result on Walsh system, we consider the system of
characters of zero-dimensional compact abelian group and give for this system a construction of a perfect $M_0$-set whose Hausdor $h$-measure equals zero, where $h$ is any non-decreasing right-continuous function taking the value zero at the origin.