Lebesgue Decomposition

Any complex measure decomposes into an absolutely continuous measure and a singular measure , with respect to some positive measure . This is the Lebesgue decomposition,

See also

Absolutely Continuous, Complex Measure, Fundamental Theorems of Calculus, Lebesgue Measure, Polar Representation, Radon-Nikodym Theorem, Singular Measure

This entry contributed by Todd Rowland

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Rowland, Todd. "Lebesgue Decomposition." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/LebesgueDecomposition.html

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