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

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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

This lesson is real analysis

Let {f_n}_n=1^∞ be a sequence of non-negative measurable functions on E.

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

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

show that lim_n→∞ ∫_E f_n= ∫_E f

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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