This lesson is real analysis Let {fn}n=1∞ be a sequence of non-negative measurable functions on E. And pointwise {fn}→f  (convergence of f)  Let suppose that for every n element of IN ,fn ≤ f  in E . show that limn→∞ ∫E fn = ∫E f

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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This lesson is real analysis

Let {fn}n=1 be a sequence of non-negative measurable functions on E.

And pointwise {fn}→f  (convergence of f) 

Let suppose that for every n element of IN ,fn ≤ f  in E .

show that limn→∞E fn = ∫E f

 

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