Measure and Integration for Probabilty
This course was created at the initiative of Mike Williams, as Math
5260 (on the quarter system) then as Math/Stat 6105 after conversion to
semesters. The intent was to provide a foundational treatment of
measure-theoretic probability for the benefit of doctoral students in
Statistics. The Math. and Stat. departments alternated teaching
it, each department teaching it two years in a row. This
continued until 2003, at which point Stat. took over teaching it every
year. It still exists as a Statistics course, but no longer as a
Mathematics course.
When the Math. dept. taught it we used the text by P. Billingsly, Probability and Measure.
There is a lot more material in that text than was covered in the
course, so I wrote a set of notes containing just the material that we
typically covered. I used those notes 1993 and 1997 when I taught
the course. Those notes are available here for download:
There was also an effort to offer a second semester, Math 6000 (Winter
quarter) and then Math 6106 (Spring semesters), to explore some further
topics in more detail. I don’t know if this was ever offered
prior to 1987 but we did offer it in the Winter quarter of 87/88 and
then in the Spring Semesters of 1990 and 1993. Selected chapters
from Billingsley were used the first two times. The last time we
used Wentzell's book, A Course in the Theory of Stochastic Processes. The course has since been discontinued.