Mathematics 420/507, Section 101

Real Analysis I/Measure Theory and Integration

Department of Mathematics, University of British Columbia

Prerequisites: A score of 68% or higher in MATH 321.

Instructor

Joel Feldman

E-mail	feldman@math.ubc.ca
Office	Math 221
Phone	604-822-5660
Home page	http://www.math.ubc.ca/~feldman/
Office hours	Mon 10:00-11:00, Tue 11:00-12:00, Thurs 2:00-3:00

Text

Gerald B. Folland, Real Analysis, Modern Techniques and Their Applications, Second edition. There is a list of errata at http://www.math.washington.edu/~folland/Homepage/reals.pdf

I will post all handouts, problem sets, etc. on the web here.

Other References

H. L. Royden, Real Analysis.
W. Rudin, Real and Complex Analysis.
E. H. Lieb and M. Loss, Analysis.

Topics

Measures (§1):
Sigma-algebras, measures
Borel and Lebesgue measures
Integration (§2):
Measurable functions, integration
Convergence, product measures
Differentiation (§3):
Signed measures, Lebesgue-Radon-Nikodym Theorem
L^p Spaces (§6):
L^p Spaces, Holder and Minkowski inequalities
Dual spaces

Grading

There will be weekly problem sets accounting for about 50% of the final mark.
The final exam will account for about 50% of the final mark.
Grades will probably be scaled.

Policies

The final examination will be strictly closed book: no formula sheets or calculators will be allowed.
There is no supplemental examination in this course.
Late homework assignments normally receive a grade of 0. Missing a homework normally results in a mark of 0. Exceptions may be granted in two cases: prior consent of the instructor or a medical emergency.