I was looking at this different version of Egoroff's Theorem: Omitting the hypotheses of finiteness of the measure in Egorov theorem.
I'm wondering if someone can show me an example where you can use this result instead of the standard one.
In particular, I'm looking for a sequence of measurable (complex-valued) functions $(f_n)_{n \in \mathbb{N}}$ on $X$ , $\mu (X) = \infty$ , such that $f_n \rightarrow f$ a.e. and $|f_n| <g \quad ,\forall n \in \mathbb{N}$ where $g$ is integrable.
Any help is appreciated. Thanks!