MATH 417 - Honors Real Variables, I (Winter 2015)

Instructor

Volker Runde

Office Hours

CAB 675, MWF 11:00-11:50 or by appointment

Content

• σ-algebras and measures;


• the measure theoretic integral (in particular, the N-dimensional Lebesgue integral;


• convergence theorems;


• prodduct measures;


• absolute continuity;


• signed measures;


• the Lebesgue-Stieltjes integral.

Textbooks

I won't require any particular textbook, but
1. D. L. Cohn, Measure Theore, Second Edition. Birkhäuser, 2013
is highly recommended. Othere books you may find useful to look into are:
1. C. D. Aliprantis and O. Burkinshaw, Principles of Real Analysis, Third Edition. Academic Press, 1998;


2. H. L. Royden and P. M. Fitzpatrick, Real Analysis, Fourth Edition. Prentice Hall, 2010;


3. T. Tao, An Introduction to Measure Theory. American Mathematical Society, 2011.

Grading

The grade will be based on (approximately) weekly homework assignments (30%), an in-class-midterm on February 13 (20%), and a final (50%). A total mark of 50% will yield a letter grade of D or better, and a total mark of 90% will result in a grade of A or better.

Course Materials