Probability and Measure

Part IID course, Michaelmas Term 2005

by Stefan Grosskinsky

Informal course description and schedule, Official page of the course, page of the 2006 course

Lecture times: MWF at 11am, Meeting Room 3

**Example sheets**

- sheet 1 (Set systems and measures)

problem 1.6: Check out wikipedia for a definition of liminf and limsup of a sequence of real numbers.
- sheet 2 (Measurable functions and integration)

problem 2.13: Check out wikipedia for a definition of sigma-finite measures.

problem 2.14: Assume X>=0 in (b) AND (c).

problem 2.12: Please assume g to be continuous instead of non-negative measurable
- sheet 3 (L
^{p}-spaces, convergence)

problem 3.8(a): In the definition of Λ(x) write φ(x) instead of M(x)
- sheet 4 (characteristic functions, Gaussian rv's, ergodic theory)

problem 4.12: considering the binary expansion of each x, you may use Borel's normal number theorem.

Then proceed as in the proof of Theorem 7.4.

**Hand-outs**

- hand-out 1 (Proof of Dynkin's lemma and Caratheodory's extension theorem)
- hand-out 2 (Convergence of random variables, Riemann integration)
- hand-out 3 (Ergodic theorems)

**Course notes:** have been removed to secure the prosperity of the 2006 course

Last updated on 10.01.2006 by Stefan Großkinsky