Theorem 8.2.10: Lebesgue's Bounded Convergence Theorem

Let { f_n } be a sequence of (Lebesgue) integrable functions that converges almost everywhere to a measurable function f. If |f_n(x)| g(x) almost everywhere and g is (Lebesgue) integrable, then f is also (Lebesgue) integrable and:

| f_n - f | dm = 0

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