Math 597, Analysis II

I like measure theory, actually. And functional analysis looks pretty cool. (I might take it next semester.)

This course is taught by Jinho Baik.

1. Measure
   • Jan. 5, intro
   • Jan. 7, $\sigma$-algebra, measures
   • Jan. 10, measures, outer measures
   • Jan. 12, outer measures, cont’d
   • Jan. 14, outer measures, Hahn-Kolmogorov theorem
   • Jan. 19, Hahn-Kolmogorov theorem
   • Jan. 21, Borel measure on $\mathbb R$
   • Jan. 24, Lebegus-Stieltjes measure
   • Jan. 26, regularity properties of L-S measures
2. Integration
   • Jan. 28, measurable functions
   • Jan. 31, integration of non-negative functions, MCT
   • Feb. 2, Fatou’s Lemma, Markov’s inequality
   • Feb. 4, integration of complex functions, DCT
   • Feb. 7, $L^1$ space, Riemann integrability
   • Feb. 9, Riemann integrability, modes of convergence
   • Feb. 11, modes of convergence
3. Product Measure
   • Feb. 14, product $\sigma$-algebra
   • Feb. 16, product measures, monotone class lemma
   • Feb. 18, Fubini-Tonelli theorem
   • Feb. 21, Lebesgue Measure on $\mathbb R^d$
4. Differentiation on Euclidean Space
   • Feb. 25, Hardy-Littlewood maximal function
   • Mar. 7, Lebesgue differentiation theorem
5. Normed Vector Spaces
   • Mar. 9, metric and normed spaces
   • Mar. 11, $L^p$ spaces
   • Mar. 14, Banach spaces
   • Mar. 16, bounded linear transformations
   • Mar. 18, dual of $L^p$ spaces
6. Signed and Complex Measures
   • Mar. 21, signed measures
   • Mar. 23, signed measures
   • Mar. 25, absolutely measurable spaces
   • Mar. 28, absolutely measurable spaces
   • Mar. 30, Lebesgue differentiation theorem for regular Borel measures
   • Apr. 1, monotone differentiation theorem
   • Apr. 4, functions of bounded variation
   • Apr. 6, functions of bounded variation
   • Apr. 8, absolutely continuous functions
7. Hilbert Spaces
   • Apr. 11, inner product spaces
   • Apr. 13, orthonormal basis
8. Intro to Fourier Analysis
   • Apr. 15, Fourier series
   • Apr. 18, Fourier series

(Things gets a bit messy after spring break. I’ll fix it as soon as possible)

(Notice on Safari the hyperlink to sections within the PDF does not work. It seems to work on Chromium-based browsers and Firefox.)