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    Lebesgue Decomposition

    Definition

    Any complex measure λ decomposes into an absolutely continuous measure λ_a and a singular measure λ_c, with respect to some positive measure μ. This is the Lebesgue decomposition, λ = λ_a + λ_c.

    Related terms

    absolutely continuous | complex measure | fundamental theorems of calculus | Lebesgue measure | polar representation | Radon-Nikodym theorem | singular measure

    Associated person

    Henri-Léon Lebesgue

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