$L^1$ functions are finite almost everywhere

Finite $L^1$ norm forces an integrable function to be finite almost everywhere.Suggest a slogan

Let $m$ be Lebesgue measure on $\RR^n$ and let $f\colon\RR^n\to[-\infty,\infty]$ be measurable with $\int_{\RR^n}\abs{f}\,dm<\infty$. Then $m\qty{\theset{x\in\RR^n\suchthat \abs{f(x)} = \infty}} = 0$.