Lecture Notes & Readings

 

The readings are assigned in the textbook
Buy at Amazon Adams, Malcolm Ritchie, and Victor Guillemin. Measure Theory and Probability. Birkha╠łuse, 1996. ISBN: 9780817638849. [Preview with Google Books]

Additional notes are provided for selected lectures to supplement the textbook.

LEC # TOPICS READINGSLECTURE NOTES
1 Coin Tossing, Law of Large Numbers, Rademacher Functions Sections 1.1 and 1.2Introductory Lecture (PDF)
2 Measure Theory, Random Models Sections 1.3 and 1.4Boolean Rings (PDF)
3 Measurable Functions, Lebesgue Integral Sections 2.1 and 2.2<no notes>
4 Convergence Theorems, Riemann Integrability Sections 2.3 and 2.4<no notes>
5 Fubini's Theorem, Independent Random Variables Sections 2.5, 2.6, and 2.7<no notes>
6 Lebesgue Spaces, Inner Products Sections 3.1 and 3.2This resource may not render correctly in a screen reader.Lp Theory (PDF)
7 Hilbert Space, Midterm Review Section 3.3Hilbert Space and Orthonormal Bases (PDF)
8 Fourier Series and their Convergence Section 3.4Fourier Series, Part 1 (PDF), This resource may not render correctly in a screen reader.Fourier Series, Part 2 (PDF)
9 Applications of Fourier Series <no readings>Fourier Series, Part 3 (PDF)
10 Fourier Integrals Section 3.5This resource may not render correctly in a screen reader.Fourier Integrals (PDF)
11 Fourier Integrals of Measures, Central Limit Theorem Section 3.8Fourier Integrals, Measures, and Central Limit Theorem (PDF)
12 Brownian Motion <no readings>This resource may not render correctly in a screen reader.Brownian Motion (PDF)
13 Brownian Motion Concluded, Review for Final Exam <no readings><no notes>