On Series by Haar System

摘要

The paper considers the series by Haar system ∞∑ n=1 a_nx_n(x). Satisfying the conditions ∞∑ n=1 a_n~2X_n~2(x) = ∞ and a_nX_n(x) → 0 almost everywhere. Some theorems about correcting a func- tion on sets of arbitrarily small measures are proved.