Dominated Convergence Theorem

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In measure theory, the dominated convergence theorem is a cornerstone of Lebesgue integration. It can be viewed as a culmination of all efforts, and is a general statement about the interplay between limits and integrals.

Statement and proof of Theorem

  • Statement: Suppose <math>\{f_n\}<math> is a sequence of measurable functions such that f_n(x) \to f(x)