Can Fatou's lemma and monotone convergence theorem be considered as equivalent?
2026-05-04 17:02:07.1777914127
Can Fatou's lemma and monotone convergence theorem be considered as equivalent?
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They can be considered equivalent in the following sense:
If ones knows Fatou's Lemma, one can prove Monotone Convergence Theorem by using it.
If one knows Monotone Convergence Theorem, one can prove Fatou's Lemma by using it.
But note that there are ways to prove the Monotone Convergence Theorem without using the Fatou's Lemma. And vice versa. Both of them follow from the other axioms and definitions of measure theory.