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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 32E
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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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