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Prove that if [itex]f \in L^1(\mathbb{R},\mathcal{B},m)[/itex] and [itex]a \in \mathbb{R}[/itex] is fixed, then [itex]F(x):=\int_{[a,x]}f\mbox{d}m[/itex] is continuous. Where [itex]\mathcal{B}[/itex] is the Borel [itex]\sigma[/itex]-algebra, and [itex]m[/itex] is a measure.

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# Homework Help: Continuity on L^1 spaces

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