On the $L^1$ and pointwise divergence of continuous functions

Karol Gryszka, Paweł Pasteczka

For a family of continuous functions $f_1,f_2,\dots :I\to \mathbb{R}$ ($I$ is a fixed interval) with $f_1\le f_2\le \dots$ define a set $$ I_f:=\big\{x \in I \colon \lim_{n…