On the closedness theorem in the theory of trigonometric series

Abstract

A very simple proof was given by Prof. V.A. Steklov, expressed by the formula, but ше still differs significantly from various proofs of the same theorem given by prof. V. A. Steklov and, rather in terms of ideas, approaches the proof of Prof. Hurwitz (based on the Cesaro-Fejer method of ariemetic averages), having, it seems to me, the advantage of greater simplicity, since it is based on the application of the theorem on term-by-term integration of trigonometric series, which itself is a special case of the closedness theorem.