ON A DIVERGENT SERIES OF MEASURABLE FUNCTIONS.

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 Σ (∣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. [ABSTRACT FROM AUTHOR]