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Exercise 4.3 If (X, A, µ) is a measure space, define * (A) = inf{µ(B) : A C B, B € A} for all subsets A of X. Show that µ* is an outer measure. Show that each set in A is u*-measurable and u* agrees with the measure µ on A.

Exercise 4.3 If (X, A, µ) is a measure space, define * (A) = inf{µ(B) : A C B, B € A} for all subsets A of X. Show that µ* is an outer measure. Show that each set in A is u*-measurable and u* agrees with the measure µ on A.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Need some help witgh outer measures for real analysis , Thanks for explaining in advance

Exercise 4.3 If (X, A, µu) is a measure space, define e* (A) = inf{(B) : AC B, B E A} for all subsets A of X. Show that u* is an outer measure. Show that each set in A is u*-measurable and u* agrees with the measure u on A.
Transcribed Image Text:Exercise 4.3 If (X, A, µu) is a measure space, define e* (A) = inf{(B) : AC B, B E A} for all subsets A of X. Show that u* is an outer measure. Show that each set in A is u*-measurable and u* agrees with the measure u on A.
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