autumn 2009 
Teacher: Torgny Lindvall, office MVH3015, phone connection: 3574,  e-mail:
The fundaments of modern probability theory were laid in the first decades of the 20:th century,
following the development of measure and integration theory. In this course, we will carefully
study the connections between
- measures and probabilities,
- integrals and expectations, and
- product spaces and independence.
A crucial role here is played by  Dynkin's lemma, using so called  pisystems, which are very
convenient and effecient to use in probability theory.
The last main topic of the course is characteristic functions (= Fourier transforms
of probability measures) and their use to prove  the central limit theorem.
Among other topics, we notice Kolmogorov's 0-1 law, and a probabilistic proof
of Weierstass' approximation theorem.

The book
to be used is:
David Williams: Probability and Expectations, Cambridge University Press.
It is available in paperback.

If you are curious about the author, you may click here :  Williams.

And you may consult the excellent site MacTutor archive to learn about the  pioneers of
measure and integration theory,  and  probability theory:  Borel, Lebesgue, Kolmogorov,
Khinchin, Levy...

The preiminary schedule is that we meet on Mondays,  10-12, and on Thursdays, 13-15.
However, if that is not suitable, then we find other hours.  The first session is on

Monday, 31 August, 10.00-11.45 in MVL15.

See you then!
Torgny Lindvall