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Measure Theory · Calculus

Convergence Theorems

The DCT — if |f_n| ≤ g (integrable) and f_n → f, then ∫f_n → ∫f — is why measure theory was invented. It licenses interchange of limits and integrals.

WHAT STUDENTS WILL LEARN
Prove the Monotone Convergence Theorem
Prove the Dominated Convergence Theorem
Apply Fatou’s Lemma
Distinguish modes of convergence
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