Probability and Measure

Part IID course, Michaelmas Term 2006

by Stefan Grosskinsky

Informal course description and schedule, Official page of the course, Last year's page

Lecture times: MWF at 10am, Meeting Room 3

**Example sheets**

- sheet 1 (Set systems and measures)

problem 1.2: atoms should be non-empty sets

problem 1.7: liminf and limsup will be discussed in class in the 6th lecture. If you cannot wait, check out wikipedia for a definition for a sequence of real numbers.
- sheet 2 (Measurable functions and integration)

problem 2.14 and 2.15: you need Fubini's theorem, see hand-out 3
- sheet 3 (Convergence, Fubini, L
^{p}-spaces)

- sheet 4 (characteristic functions, Gaussian rv's, ergodic theory)

**Hand-outs**

- hand-out 1 (Proof of Caratheodory's extension theorem)
- hand-out 2 (Convergence of random variables)
- hand-out 3 (Connection between Lebesgue and Riemann integration)
- hand-out 4 (Ergodic theorems)

At the end of the proof of Birkhoff's theorem μ(f)=∫f dμ (changed in above version to the usual notation)

**Course notes:** (preliminary version of the whole thing) notes06.pdf (updated 19.1.06)

NEW: non-examinable material listed in the introduction

happy reading... and please let me know about errors. I am also very happy about other comments.

Last updated on 19.1.2006 by Stefan Großkinsky