The Monotone Convergence Theorem states that if a sequence of measurable functions is non-decreasing and converges pointwise to a limit function, then the integral of the limit function equals the limit of the integrals of the functions in the sequence. This theorem is crucial in the context of Lebesgue measure and integration because it provides a powerful way to interchange limits and integrals, facilitating the evaluation of certain integrals that would be challenging to compute directly.
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