Consider the (Ï-finite) measure space ((, A, μ), and let {Ai, i = 1, 2,....} be a

Consider the (σ-finite) measure space ((, A, μ), and let {Ai, i = 1, 2,....} be a (measurable) partition of (. For each i, define the measure μi by: μi (A) = μ (A ( Ai). Then, if X is a r.v. defined on ((, A, μ) for which the integral ( Xd μ exists, show that the integrals ( Xd μ, i ( 1, also exist and

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EIS Xdµ¡ = § Xdµ Хаи Σ. Li=1 !ntpx