MA598R’07: Calendar

Monday, June 11
Riemann-Stieltjes Integral

• Functions of Bounded Variation
• Existence of the Riemann-Stieltjes Integral
• The Riemann-Stieltjes Integral and Limits

Wednesday, June 13
Abstract Measures. Lebesgue Measure.

• Algebras and σ-algebras of Sets
• Additive Set Functions and Measures
• Properties of Measures
• Lebesgue Measure on Rⁿ
• The Cantor Set

Monday, June 18
Second chances: review of Measure Theory

Wednesday, June 20
Measurable Functions

• Elementary Properties of Measurable Functions
• Structure of Measurable Functions
• Sequences of Measurable Functions

Monday, June 25
Second chances: review of Measurable Functions.

Wednesday, June 27
Integration

• The Integral of Nonnegative Functions
• The Integral of Arbitrary Functions
• Riemann and Lebesgue Integrals
• Metric structure of L₁
• The Lebesgue Differentiation Theorem

Monday, July 2
Second chances: review of Integration

Wednesday, July 4
No class

Monday, July 9
Third chances: review of Integration

Wednesday, July 11
L_p Spaces

• The Lebesque L_p spaces
• Functionals on L_p
• Weak convergence

Monday, July 16
Second chances: review of L_p spaces

Wednesday, July 18
Advanced Topics:

• Covering Lemmas.
• Absolute Continuity.
• Approximations to the Identity.
• The Fourier Transform.

Monday, July 23
Second chances: review of Advanced Topics.

Wednesday, July 25
Qual frenzy

Monday, July 30
Qual frenzy