Editing Dominated convergence theorem (section)

{{More footnotes needed|section|date=September 2024}}

{{Short description|Theorem in measure theory}}
In [[measure theory]], [[Henri Lebesgue|Lebesgue]]'s '''dominated convergence theorem''' gives a mild [[sufficient condition]] under which limits and integrals of a sequence of functions can be interchanged. More technically it says that if a [[sequence]] of functions is bounded in absolute value by an integrable function and is [[almost everywhere]] pointwise [[convergence (mathematics)|convergent]] to a [[Function (mathematics)|function]] then the sequence converges in <math>L_1</math> to its pointwise limit, and in particular the integral of the limit is the limit of the integrals. Its power and utility are two of the primary theoretical advantages of [[Lebesgue integral|Lebesgue integration]] over [[Riemann integral|Riemann integration]].

In addition to its frequent appearance in mathematical analysis and partial differential equations, it is widely used in [[probability theory]], since it gives a sufficient condition for the convergence of [[expected value]]s of [[random variable]]s.