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