: Let<ƒ„> be a sequence of summable functions on a set es in measure to f and if the family of integrals of fis mable on E and

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 74E
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Theorem 15. (Vitali's Theorem): Let <fn> be a sequence of summable functions on a set
E with finite measure. If <f> converges in measure to f and if the family of integrals of fis
absolutely equi-continuous, then f is summable on E and
lim f f (x) dx = f(x) dx.
11-00
Transcribed Image Text:Theorem 15. (Vitali's Theorem): Let <fn> be a sequence of summable functions on a set E with finite measure. If <f> converges in measure to f and if the family of integrals of fis absolutely equi-continuous, then f is summable on E and lim f f (x) dx = f(x) dx. 11-00
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