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Math Help - hahn decomposition

  1. #1
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    hahn decomposition

    I've got the following problem to solve:

    let λ be σ-additive set function defined in the algebra m of subsets of X. Suppose that f:X -> R is measurable and the integral int_X (f)dλ exists, k(a) = int_A (f)dλ (A ∈ m) is σ-additive set function.

    Find Hanh decomposition of X with respect to function k.

    Is there any universal workflow of determining such decomposition. What should I pay attention to?
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  2. #2
    Super Member Rebesques's Avatar
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    Re: hahn decomposition

    Universal Workflow
    Alas, no Royal Road to Geometry.

    P=\{f\geq 0\}, N=\{f\leq 0\}
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