MATH 471 Notes
This page has some instructors notes. These should be useful only if you have missed class.
- Why the Riemann integral is unsatisfactory
- General Measures
- Caratheodory Outer Measure
- Caratheodory-Hahn
- Simple approximation, Fatou, Monotone Convergence Theorem
- Non measurable sets
- Cantor set, Devils-staircase
- Littlewood’s 3 principles, Luzin
- Differentiation, Hardy-Littlewood function, Lebesgues Theorem
- Signed measures and Hahn-Jordan decomposition
- Radon-Nikodym theorem
- Rudins Fundamental Theorem of Calc
- Product Measure and Fubini-Tonelli
- Convergence in Measure
- Metrics, norms, Banach spaces
- Hahn-Banach Theorem
- Baire Category, Open Mapping, Closed Graph
- Young, Holder, Minkowski
- Lp is a Banach space
- Axler 7B partial