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Theorem 6.7 (Fatou's Lemma.) Let {fn) be a sequence of non- negative, measurable functions on a set E. If {fn} converges to f a.e. on E, then Lim inf SAx)dx < É Sf.(x)dx n00

Theorem 6.7 (Fatou's Lemma.) Let {fn) be a sequence of non- negative, measurable functions on a set E. If {fn} converges to f a.e. on E, then Lim inf SAx)dx < É Sf.(x)dx n00

Algebra & Trigonometry with Analytic Geometry
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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Theorem 6.7 (Fatou's Lemma.) Let {fn} be a sequence of non- negative, measurable functions on a set E. If {fn} converges to f a.e. on E, then Lim inf Sfx)dx < É Sf.(x)dx n00
Transcribed Image Text:Theorem 6.7 (Fatou's Lemma.) Let {fn} be a sequence of non- negative, measurable functions on a set E. If {fn} converges to f a.e. on E, then Lim inf Sfx)dx < É Sf.(x)dx n00
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