Previously, we wrote a blog post about Weierstrass M Test. It turns out Weierstrass M Test is a special case of Lebesgue’s Dominated Convergence Theorem, a very powerful theorem in Measure Theory, where the measure is taken to be the counting measure.
Lebesgue Dominated Convergence Theorem: Let be a sequence of integrable functions which converges a.e. to a real-valued measurable function . Suppose that there exists an integrable function such that for all . Then, is integrable and .
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