множество единственности

On the Uniqueness of Series with Respect to Characters of Dyadic Groups

Authors: Polyakova N.

Conditions on series with respect to characters of dyadic groups are specified by which finite or countable set is the set of uniqueness.

Martingales and Theorems of Cantor–Young–Bernstein and de la Vallée Poussin

Authors: Plotnikov M. G., Plotnikova J. A.

Uniqueness problems for one-dimensional Haar series and for multiple ones have understood in numerous works. It is well-known that the subsequence of the partial sums S2k of an arbitrary Haar series can be represented as a discrete-time martingale on some filtered probability space (­Ω, F, (Fk), P). In paper the concept of a U -set for martingales is presented and some uniqueness theorems for martingales on arbitrary compact filtered probability spaces are established.

A U-set for system of character of the zero-dimensional group under convergent over cubes

Authors: Yurchenko I. S.

 In this work we consider system of characters of the compact zero-dimensional group G and study uniqueness sets forN-fold multiple series for system of character a zero-dimensional group under convergent over cubes (in other words, U-sets). We proof that every finite set is a U-set and show that countable set with only one limit point is a U-set.