Lebesgue's Dominated Convergence Theorem

Suppose that {f_n} is a sequence of measurable functions, that f_n->f pointwise almost everywhere as n->infty, and that |f_n|<=g for all n, where g is integrable. Then f is integrable, and


See also

Almost Everywhere Convergence, Measure Theory, Pointwise Convergence

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Browder, A. Mathematical Analysis: An Introduction. New York: Springer-Verlag, 1996.

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Lebesgue's Dominated Convergence Theorem

Cite this as:

Weisstein, Eric W. "Lebesgue's Dominated Convergence Theorem." From MathWorld--A Wolfram Web Resource.

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