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Some context: I had previously asked the post below on MSE, but someone suggested I ask it here and delete the original post. In section 7 of the paper Integrals with values in Banach Spaces and ...

Lebesgue's differentiation theorem states that if $x$ is a point in $\mathbb{R}^n$ and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a Lebesgue integrable function, then the limit of $\frac{\int_B f d\...