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(1) Write the definition of a measurable set ECR. (2) By writing the definition of the measurability of ECR with the set A replaced by EUA, show that m* (EUA) = m(E) + m²(AE). (3) Let ECR be a measurable set and ACR any subset. Deduce that m* (EUA) +m*(En A) = m(E) +m*(A).

(1) Write the definition of a measurable set ECR. (2) By writing the definition of the measurability of ECR with the set A replaced by EUA, show that m* (EUA) = m(E) + m²(AE). (3) Let ECR be a measurable set and ACR any subset. Deduce that m* (EUA) +m*(En A) = m(E) +m*(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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Exercise 1 (1) (2) Write the definition of a measurable set ECR. By writing the definition of the measurability of ECR with the set A replaced by EUA, show that m* (EUA) = m(E) +m*(AE). Let ECR be a measurable set and ACR any subset. Deduce that m* (EUA) + m*(EA) = m(E) +m* (A). (3)
Transcribed Image Text:Exercise 1 (1) (2) Write the definition of a measurable set ECR. By writing the definition of the measurability of ECR with the set A replaced by EUA, show that m* (EUA) = m(E) +m*(AE). Let ECR be a measurable set and ACR any subset. Deduce that m* (EUA) + m*(EA) = m(E) +m* (A). (3)
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