Lebesgue's Dominated Convergence Theorem -- from Wolfram MathWorld

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Lebesgue's Dominated Convergence Theorem

Suppose that ${f_n}$ is a sequence of measurable functions, that pointwise almost everywhere as , and that for all , where is integrable. Then is integrable, and

REFERENCES:

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

CITE THIS AS:

Weisstein, Eric W. "Lebesgue's Dominated Convergence Theorem." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/LebesguesDominatedConvergenceTheorem.html