The Dominated Convergence Theorem is a fundamental result in measure theory and integration that allows one to interchange limits and integrals under certain conditions. Specifically, it states that if a sequence of measurable functions converges almost everywhere to a function and is dominated by an integrable function, then the integral of the limit is equal to the limit of the integrals. This theorem is especially important when dealing with uniformly convergent series as it helps in evaluating the convergence of integrals that may not be straightforward.
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