My lecturer has said that beppo levi means for and increasing sequence of X(adsbygoogle = window.adsbygoogle || []).push({}); _{i}where X_{i}is simple for all i, it holds that

∫lim_{i → ∞}X_{i}dP = lim_{i → ∞}∫X_{i}dP

But why is it that he later says things like

∫ lim_{i→ ∞}Ʃ^{i}_{n=1}P_{2}(B_{w1n})dP_{1}(w1) = lim_{i → ∞}Ʃ^{i}_{n=1}∫P_{2}(B_{w1n})dP_{1}(w1)

is a result of beppo levi? Where in beppo levi does it say you can move the sum out of the integral?!

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# Beppo-Levi relation to Sums

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