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
BUILDS ON
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