Real Analysis dealing with Measures. Exercise 3.5 Prove that if µ1, µ2, ... are measures on a measur-able space and a1, a2, . .. E [0, ), then E-1 anfln is also a mea-sure.For this exercise you may use the fact from undergraduate anal-ysis thatΣΣ+ΣΣCiji=1 j=1j=1 i=1provided each of the cij is a non-negative real or equal to +o.(This will also be a consequence of the Fubini theorem of Chapter11.)

Definition: Let X be a set and Σ a σ-algebra over X. A function μ from Σ to the extended real number…

Answered: Exercise 3.5 Prove that if µ1, µ2, . ..…

Advanced Engineering Mathematics

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Chapter2: Second-order Linear Odes

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Exercise 3.5 Prove that if µ1, µ2, . .. are measures on a measur- able space and a1, a2,. .. E [0, ∞), then n=1anfln is also a mea- sure.