Class Times, Days, and Place: 10:00-10:50 MWF, Deady Hall
206
Instructor: Hao Wang
Textbook: Instructor's Lecture Notes
Reference Book: (1) Measure Theory by P. R. Halmos;
(2) Probability and Measure by Patrick Billingsley
(3) Measure Theory by Donald L. Cohn
(4) Brownian Motion and Stochastic Calculus by I. Karatzas, S.E.
Shreve
Office: 11A Deady Hall
Office Hours: M:11:00-12:00pm and W:11:00-12:00pm (Otherwise,
you need to make an appointment with me by e-mail.)
Web URL:
http://darkwing.uoregon.edu/~haowang/teaching/671_FALL2005/671.html
Tentative Coverage: This course is intended to cover
following
contents:
(1) Classes of subsets
(2) Extension of measure
(3) Measurable space, measurable functions \pi-\lambda system
(4) Integral
(5) Different convergences
(6) Measurable transformations
(7) Product of measurable spaces , Fubini's Theorem, Kolmogorov's
Theorem
(8) Conditional probability and expectation
(9) L^p Space
Homework and presentations: Since this is an advanced
probability
course, we will arrange that the activities of learning and doing
research
are combined together. Some questions and problems with different
degrees of challenging are assigned as homework questions or
research
questions. In order to well digest the contents of this course and
improve
the research ability, during the term, two or three times of
homework
presentations or question discussions will be organized. Homework
is due weekly before Monday's lecture. Homeworks and presentations will
partially contribute to your final grade.