MAS350/451/6352 MEASURE AND PROBABILITY
Background Information
Lecturer: Dave Applebaum (I 14) – ext 23703 d.applebaum@sheffield.ac.uk
Office hours: Monday 11am and Friday 10am, but you can come at other times – best to
make appointment by e-mail.
Measure theory is the abstract mathematical theory that underlies all models of measurement
in the real world. This includes measurement of length, area and volume, mass but also
chance/probability. Measure theory is on the one hand a branch of pure mathematics, but it
also plays a key role in many applied areas such as physics and economics. In particular it
provides a foundation for both the modern theory of integration and also the theory of
probability. It is one of the milestones of modern analysis and is an invaluable tool for
functional analysis.
Assessment: 100% exam (not open book). The two previous years’ exams are posted on the
module webpage to help with revision.
Problem Sheet: It is advised to attempt all questions. Worked solutions to problems will be
posted – usually in the week after we finish the relevant chapter.
Formative work: Three sets of exercises (taken from the problem sheet) are to be handed in
for marking to give you feedback on progress.
Syllabus
Topic
Measure spaces and measure
Measurable functions
Lebesgue integration
Probability and measure
Weeks
1,2
3, 4
5,6,7,8
9,10,11
Course webpage: http://www.applebaum.staff.shef.ac.uk/MPindex.html
Students taking MAS451/6352 have some additional reading and extra problems to work on.
This year (2015-16), the topic is “Product Measures and Fubini’s theorem,” and the best time
to work on it is after we have finished Chapter 3.