MATH 471 Notes

This page has some instructors notes. These should be useful only if you have missed class.

  1. Why the Riemann integral is unsatisfactory
  2. General Measures
  3. Caratheodory Outer Measure
  4. Caratheodory-Hahn
  5. Simple approximation, Fatou, Monotone Convergence Theorem
  6. Non measurable sets
  7. Cantor set, Devils-staircase
  8. Littlewood’s 3 principles, Luzin
  9. Differentiation, Hardy-Littlewood function, Lebesgues Theorem
  10. Signed measures and Hahn-Jordan decomposition
  11. Radon-Nikodym theorem
  12. Rudins Fundamental Theorem of Calc
  13. Product Measure and Fubini-Tonelli
  14. Convergence in Measure
  15. Metrics, norms, Banach spaces
  16. Hahn-Banach Theorem
  17. Baire Category, Open Mapping, Closed Graph
  18. Young, Holder, Minkowski
  19. Lp is a Banach space
  20. Axler 7B partial