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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b19024a-5609-4e35-a0a7-7058d3f26c57%2F8414e6ea-585f-4de0-ae36-a57eca3c02f8%2F8auwee_processed.png&w=3840&q=75)
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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