I have a Lebesgue measurable function $f:X\rightarrow \mathbb{R}$ where $X\subset\mathbb{R}$. Is there an open set $X^O$ such that \begin{equation*} \int_X f=\int_{X^O} f \end{equation*} and $X^O$ is very similar to $X$ in some sense?
2026-04-22 11:29:07.1776857347
Can I approximate a measurable set with an open set for integration purposes?
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