Let (*S, F, μ)* be a measure space. Here S is a set, F is a *σ*-algebra, *µ* is a *σ*-finite measure on F. If *F*_{0} is a *σ*-subalgebra of F, *x**∈**L*_{1} (*(S*, *F*, *μ*), then denote by *E*_{Fo} the unique, up to equivalence, *F*_{0}-measurable function satisfying
for each *A ∈ F*_{0}. By the Radon — Nikodym theorem, such function exists. The function *E*_{Fo}*x =**E*_{Fo,μ}*x* is called the conditional expectation with respect to *F*_{0}.