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Let fn be a sequence of non-negative integrable Lebesgue functions on the interval (0,10) such that fn (x) → f(x) almost for all x € (0,10). Let he Proof that: 10 [₁°F + F Hint: use Fatou's motto. F(x) = ffdm F₂(x) = f* fnc 0 fndm 10 of from (f+F) dm ≤ lim inf n→ 00 (n + Fn) dm

Let fn be a sequence of non-negative integrable Lebesgue functions on the interval (0,10) such that fn (x) → f(x) almost for all x € (0,10). Let he Proof that: 10 [₁°F + F Hint: use Fatou's motto. F(x) = ffdm F₂(x) = f* fnc 0 fndm 10 of from (f+F) dm ≤ lim inf n→ 00 (n + Fn) dm

Advanced Engineering Mathematics
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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Let fn be a sequence of non-negative integrable Lebesgue functions on the interval (0,10) such that fn (x) → f(x) almost for all x € (0,10). Let he Proof that: 10 6²0 Hint: use Fatou's motto. F(x) = f* fdm F₂(x) = [*fndm (f+F) dm ≤ lim inf n→∞0 10 [°C (fn + Fn) dm
Transcribed Image Text:Let fn be a sequence of non-negative integrable Lebesgue functions on the interval (0,10) such that fn (x) → f(x) almost for all x € (0,10). Let he Proof that: 10 6²0 Hint: use Fatou's motto. F(x) = f* fdm F₂(x) = [*fndm (f+F) dm ≤ lim inf n→∞0 10 [°C (fn + Fn) dm
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