- #1
stukbv
- 118
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My lecturer has said that beppo levi means for and increasing sequence of Xi where Xi is simple for all i, it holds that
∫limi → ∞XidP = limi → ∞∫XidP
But why is it that he later says things like
∫ limi→ ∞ Ʃin=1P2(Bw1n)dP1(w1) = limi → ∞Ʃin=1∫P2(Bw1n)dP1(w1)
is a result of beppo levi? Where in beppo levi does it say you can move the sum out of the integral?!
∫limi → ∞XidP = limi → ∞∫XidP
But why is it that he later says things like
∫ limi→ ∞ Ʃin=1P2(Bw1n)dP1(w1) = limi → ∞Ʃin=1∫P2(Bw1n)dP1(w1)
is a result of beppo levi? Where in beppo levi does it say you can move the sum out of the integral?!