(i) Consider the measure space ((, A, ) and let C be a fixed set in A On A, define the function o by o (A) (A ( C) Then show that o is a measure (ii) Let X a r v defined on ((, A, ) and suppose that ( Xd exists Then show that ( Xd o also exists and that ( Xd o (C Xd

Question: (i) Consider the measure space ((, A, ) and let C be a fixed set in A. On A, define the function o by: o

(i) Consider the measure space ((, A, μ) and let C be a fixed set in A. On A, define the function μo by: μo (A) = μ (A ( C). Then show that μo is a measure.
(ii) Let X a r.v. defined on ((, A, μ) and suppose that ( Xd μ exists. Then show that ( Xd μo also exists and that ( Xd μo = (C Xd μ.

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