The readings are assigned in the textbook

Adams, Malcolm Ritchie, and Victor Guillemin. *Measure Theory and Probability*. Birkhäuse, 1996. ISBN: 9780817638849. [Preview with Google Books]

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

LEC # | TOPICS | READINGS | LECTURE NOTES |
---|---|---|---|

1 | Coin Tossing, Law of Large Numbers, Rademacher Functions | Sections 1.1 and 1.2 | Introductory Lecture (PDF) |

2 | Measure Theory, Random Models | Sections 1.3 and 1.4 | Boolean 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 3.2 | Lp Theory (PDF) |

7 | Hilbert Space, Midterm Review | Section 3.3 | Hilbert Space and Orthonormal Bases (PDF) |

8 | Fourier Series and their Convergence | Section 3.4 | Fourier Series, Part 1 (PDF), Fourier Series, Part 2 (PDF) |

9 | Applications of Fourier Series | <no readings> | Fourier Series, Part 3 (PDF) |

10 | Fourier Integrals | Section 3.5 | Fourier Integrals (PDF) |

11 | Fourier Integrals of Measures, Central Limit Theorem | Section 3.8 | Fourier Integrals, Measures, and Central Limit Theorem (PDF) |

12 | Brownian Motion | <no readings> | Brownian Motion (PDF) |

13 | Brownian Motion Concluded, Review for Final Exam | <no readings> | <no notes> |