STRUCTURE OF THE SET OF SUMS OF A CONDITIONALLY CONVERGENT SERIES IN A NORMED SPACE

Abstract

Conditions are investigated for the set of sums of a conditionally convergent series with terms in a normed space to be linear. Main result: if is a conditionally convergent series such that converges for almost all , then the set of sums of the series is linear ( is the sequence of Rademacher functions).Bibliography: 24 titles.