Overview
Given a set of functions {% f_1 \ll f_2 \ll ... \ll f_n %} such that {% f_i(x) \rightarrow f(x) %} for all {% x %} and there is a function {% g \in \mathcal{L}^1 %} such that
{% | f_i(x) | \leq g(x) %}
(that is {% f %} is dominated by {% g %})
then
{% f_i \rightarrow f %}