
Radon-Nikodym theorem,
n. the theorem that, given a sigma-finite measure μ and a signed measure λ that is absolutely continuous with respect to μ, there is a function f that possesses a Lebesgue integral, such that, for each measurable set E,
, over Ethat is unique (up to a set with μ-measure zero); this function is called the Radon-Nikodym derivative of λ with respect to μ, and is denoted dλ/dμ. These notions are used in the general definitions of conditional expectation and conditional probability.
, over E