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
Lp Spaces

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

Monday, July 16
Second chances: review of Lp 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

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