Let {fn}n>1 and {9n}n≥1 be measurable functions on (S,F,μ) to R and an (w) ↑ f(w) for all w & S. Ther

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 55E
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M3

Let {fn}n>1 and {9n}n>1 be two sequences of simple
nonnegative measurable functions on (S,F,u) to R+ such that as n →∞0,
fn (w) ↑ f(w) and gn (w) ↑ f(w) for all w En. Then
lim
| fndμ = lim
818
lim Ind.
Transcribed Image Text:Let {fn}n>1 and {9n}n>1 be two sequences of simple nonnegative measurable functions on (S,F,u) to R+ such that as n →∞0, fn (w) ↑ f(w) and gn (w) ↑ f(w) for all w En. Then lim | fndμ = lim 818 lim Ind.
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