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anonymous
 one year ago
I need help please to prove some properties of a positive measure which are
(a)Let µ be a positive measure on a measurable space (X,M). Let c > 0. Prove that ˜µ = cµ is also a measure
(b) Let µ1, µ2 be two positive measures on a measurable space. Assume also that there is at least one set A ∈ M such that µ1(A) + µ2(A) < ∞.
Prove that ˆµ = µ1 + µ2 is also a measure
anonymous
 one year ago
I need help please to prove some properties of a positive measure which are (a)Let µ be a positive measure on a measurable space (X,M). Let c > 0. Prove that ˜µ = cµ is also a measure (b) Let µ1, µ2 be two positive measures on a measurable space. Assume also that there is at least one set A ∈ M such that µ1(A) + µ2(A) < ∞. Prove that ˆµ = µ1 + µ2 is also a measure

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@oldrin.bataku could you help me with this question please?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this is a good place to start http://www.math.uah.edu/stat/prob/Measure.html https://en.wikipedia.org/wiki/Measure_%28mathematics%29 but i still can't solve it!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Given µ is a positive measure. Define cµ = c* (µ (A) ) , where A is a set . Claim: cµ is a positive measure Proof: 1. cµ ( ∅ ) = c * ( µ ( ∅ ) ) = c * 0 = 0 2. cμ(⋃i∈IAi)=∑i∈Icμ(Ai) cμ(⋃i∈IAi)=c⋅(μ(⋃i∈IAi))=c⋅∑i∈Iμ(Ai)=∑i∈Icμ(Ai)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is that correct for part a?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you should also show that scaling by \(c>0\) preserves nonnegativity but yes
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