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-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)