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Show that if A, B E M with m(A), m(B) <∞ then m(AUB) = m(A) +m(B) - m(AB). Show that if A, B, C M with m(A), m(B), m(C) < x then m(AUBUC) = m(A) +m(B) +m(C) - m(An B)-m(ANC)-m(BNC) +m(AnBnC).

Show that if A, B E M with m(A), m(B) <∞ then m(AUB) = m(A) +m(B) - m(AB). Show that if A, B, C M with m(A), m(B), m(C) < x then m(AUBUC) = m(A) +m(B) +m(C) - m(An B)-m(ANC)-m(BNC) +m(AnBnC).

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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Let M be the set of all measurable sets and m is the Lebesgue measure on R. (a) Show that if A, B M with m(A), m(B) < ∞ then m(AUB) = m(A) +m(B) = m(An B). Show that if A, B, C EM with m(A), m(B), m(C) <∞ then m(AUBUC) = m(A) +m(B) +m(C) (b) (c) sets. - m(AnB)-m(ANC) - m(BNC) +m(AnBnC). Find and prove a corresponding formula for the measure of the union of n
Transcribed Image Text:Let M be the set of all measurable sets and m is the Lebesgue measure on R. (a) Show that if A, B M with m(A), m(B) < ∞ then m(AUB) = m(A) +m(B) = m(An B). Show that if A, B, C EM with m(A), m(B), m(C) <∞ then m(AUBUC) = m(A) +m(B) +m(C) (b) (c) sets. - m(AnB)-m(ANC) - m(BNC) +m(AnBnC). Find and prove a corresponding formula for the measure of the union of n
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