On a Divergent Series of Measurable Functions

Abstract

Let (t _n (t)) be the sequence of trigonometric functions on [0, 1] with real scalars. We prove a generalization of the likely known result: – for every p ≥ 1 the series ∑(|t _n (t)| ^p )/n is unbounded on every set A with positive measure. This provides an alternate proof of a result in a recent paper of the author; the methods used are classical.