Lebesgue's decomposition theorem
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In mathematics, more precisely in measure theory, Lebesgue's decomposition theorem is a theorem which states that given μ and ν two σ-finite signed measures in a measurable space (Ω,Σ), there exist two σ-finite signed measures ν0 and ν1 such that:
(that is, ν0 is absolutely continuous with respect to μ)
(that is, ν1 and μ are singular).
These two measures are uniquely determined.
This article incorporates material from Lebesgue decomposition theorem on PlanetMath, which is licensed under the GFDL.
