Lebesgue's decomposition theorem
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In mathematics, more precisely in measure theory, Lebesgue's decomposition theorem[1][2][3] states that for every two σ-finite signed measures and on a measurable space there exist two σ-finite signed measures and such that:
- (that is, is absolutely continuous with respect to )
- (that is, and are singular).
These two measures are uniquely determined by and