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Exercise 3.9 Suppose X is the set of real numbers, B is the Borel 0-algebra, and m and n are two measures on (X,B) such that m((a, b)) = n((a, b)) < ∞ whenever -o < a

Exercise 3.9 Suppose X is the set of real numbers, B is the Borel 0-algebra, and m and n are two measures on (X,B) such that m((a, b)) = n((a, b)) < ∞ whenever -o < 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 assistance with measures for real analysis and Borrel sigma algebras. Thanks so much for explaining.

22 CHAPTER 3. MEASURES Exercise 3.9 Suppose X is the set of real numbers, B is the Borel 0-algebra, and m and n are two measures on (X,B) such that m((a, b)) = n((a, b)) < ∞ whenever -0 < a < b < oo. Prove that m(A) = n(A) whenever A E B. < a <b < ∞. Prove that
Transcribed Image Text:22 CHAPTER 3. MEASURES Exercise 3.9 Suppose X is the set of real numbers, B is the Borel 0-algebra, and m and n are two measures on (X,B) such that m((a, b)) = n((a, b)) < ∞ whenever -0 < a < b < oo. Prove that m(A) = n(A) whenever A E B. < a <b < ∞. Prove that
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