Exercise 5. Let (E,T) be a measurable space, let (m,)ısisn be n measures on (E,T), and le (a;)ısisn be real positive numbers. For A ET, we let m(A) = Ea;m;(A). %3D i=1 Show that m is a measure on (E, T).

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Exercise 5. Let (E,T) be a measurable space, let (m;)1sisn be n measures on (E, T), and let
(a;)1sisn be real positive numbers. For A € T, we let
m(A)Σαιm (A).
i=1
Show that m is a measure on (E,T).
Transcribed Image Text:Exercise 5. Let (E,T) be a measurable space, let (m;)1sisn be n measures on (E, T), and let (a;)1sisn be real positive numbers. For A € T, we let m(A)Σαιm (A). i=1 Show that m is a measure on (E,T).
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