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Questions about abstract measure and Lebesgue integral theory. Also concerns such properties as measurability of maps and sets.
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Composed function made Lebesgue integrable?
Let $p(x)$ be a probability density function on the unbounded set $X \subseteq \mathbb{R}^n$, so that $\int_X p(x) dx = 1$.
Let $F: X \rightarrow \mathbb{R}_{\geq 0}$ a measurable but non-integrable …