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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@oldrin.bataku could you help me with this question please?
this is a good place to start
but i still can't solve it!
Given µ is a positive measure.
Define cµ = c* (µ (A) ) , where A is a set .
Claim: cµ is a positive measure
1. cµ ( ∅ ) = c * ( µ ( ∅ ) ) = c * 0 = 0