- You are here:
Hours - Lecture:
Hours - Lab:
Hours - Recitation:
Hours - Total Credit:
Every fall semester
Lebesgue measure and integration, differentiation, abstract measure theory.
This course is equivalent to MATH 6579. Students should not be able to obtain credit for both MATH 6579 and MATH 6337.
MATH 4317 or consent of the School
At the level of Heil, “Introduction to Real Analysis” or Wheeden and Zygmund, “Measure and Integral.”
- Exterior measure, Lebesgue measure, Carath´eodory’s criterion.
- Integration: measurable functions, Egorov’s Theorem, integrals, Monotone Convergence Theorem, Fatou’s Lemma, Dominated Convergence Theorem, Fubini’s Theorem.
- Differentiation: bounded variation, Lebesgue Differentiation Theorem, absolute continuity, the Fundamental Theorem of Calculus.
- Measures: σ-algebras, positive measures, outer measures, Borel measures.
- Decomposition and differentiation of measures: Signed measures, Radon–Nikodym Theorem.