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Exercise 4.6 Let m be Lebesgue measure. Suppose for each n, An is a Lebesgue measurable subset of [0, 1]. Let B consist of those points x that are in infinitely many of the An. (1) Show B is Lebesgue measurable. (2) If m (A O for each n show m(B) 8

Exercise 4.6 Let m be Lebesgue measure. Suppose for each n, An is a Lebesgue measurable subset of [0, 1]. Let B consist of those points x that are in infinitely many of the An. (1) Show B is Lebesgue measurable. (2) If m (A O for each n show m(B) 8

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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need some assistance with real analysis showing lebesgue measurable, Thanks for any help you can provide.

Exercise 4.6 Let m be Lebesgue measure. Suppose for each n, An is a Lebesgue measurable subset of [0, 1]. Let B consist of those points x that are in infinitely many of the An. (1) Show B is Lebesgue measurable. (2) If m(An) > 8 > 0 for each n, show m(B) > 8.
Transcribed Image Text:Exercise 4.6 Let m be Lebesgue measure. Suppose for each n, An is a Lebesgue measurable subset of [0, 1]. Let B consist of those points x that are in infinitely many of the An. (1) Show B is Lebesgue measurable. (2) If m(An) > 8 > 0 for each n, show m(B) > 8.
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