Proving Monotone Convergence Theorem with Fatou’s Lemma
Nathan
The statement of the Monotone Convergence Theorem reads: Suppose that the set is measurable, and let be a sequence of non-negative, measurable functions such that, for , Let be defined by as . Then, In this proof, Fatou’s lemma will be assumed. Notice that implies that and so by Fatou’s lemma, for Now, since , … Continue reading Proving Monotone Convergence Theorem with Fatou’s Lemma →