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hw7 - f almost everywhere on A then it converges to f in...

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Math 318 HW #7 Due 5:00 PM Thursday, March 24 Reading: Wilcox & Myers § 17–19. Problems: 1. Exercise 20.12. 2. Exercise 20.16. 3. We say that a sequence ( f n ) defined on a measurable set A R converges in measure to a function f : A R if lim n →∞ m { x A : | f n ( x ) - f ( x ) | ≥ δ } = 0 for all δ > 0. (a) Show that if ( f n ) converges to
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Unformatted text preview: f almost everywhere on A , then it converges to f in measure (cf. Exercise 20.26). (b) Suppose ( f n ) converges in measure to f on A . Show that ( f n ) converges in measure to a function g if and only if f = g (a.e.). 4. Exercise 20.36. 1...
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