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e functions supnen fn, inf s (F, B(R))-measurable. limn→∞o fn (w) exists a = (limn→∞ fn) IA is (F,

e functions supnen fn, inf s (F, B(R))-measurable. limn→∞o fn (w) exists a = (limn→∞ fn) IA is (F,

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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For each n E N, let fn → R be a (F,B(R))- measurable function. (i) Then, each of the functions supnen fn, infnen fn, lim supn→∞o fn, and lim infn oo fn is (F, B(R))-measurable. (ii) The set A = {w : limn→∞o fn(w) exists and is finite} lies in F and the function h = (limn→∞ fn) · IA is (F, B(R))-measurable.
Transcribed Image Text:For each n E N, let fn → R be a (F,B(R))- measurable function. (i) Then, each of the functions supnen fn, infnen fn, lim supn→∞o fn, and lim infn oo fn is (F, B(R))-measurable. (ii) The set A = {w : limn→∞o fn(w) exists and is finite} lies in F and the function h = (limn→∞ fn) · IA is (F, B(R))-measurable.
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