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.

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

Henri-Léon Lebesgue