Let u be a positive measure on a measure space X. Assume that E, E,... are...

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Let u be a positive measure on a measure space X. Assume that E₁, E₂,... are measurable subsets of X with the property that for n is not equl to m, u(En n Em) = 0. Let E be the union of these sets. Prove that μ(Ε) = Σμ(En) n=1 Let u be a positive measure on a measure space X. Assume that E₁, E₂,... are measurable subsets of X with the property that for n is not equl to m, u(En n Em) = 0. Let E be the union of these sets. Prove that μ(Ε) = Σμ(En) n=1

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