Summary: Real Variables I: Math 607
Fall 2011, TR 3:555:10 in Blocker 164
Professor: Michael Anshelevich, Milner 326, email@example.com.
Office hours: M 23 p.m., TR 2:203:20 p.m., or by appointment.
Textbook: Folland, REAL ANALYSIS, MODERN TECHNIQUES AND THEIR APPLICATIONS, 2nd
ed., Wiley, ISBN 0471317160.
Prerequisites: Math 447 or equivalent. Particularly, Lebesgue integration on the real line (rather
than on abstract measure spaces), and analysis on metric spaces (rather than on topological spaces).
Learning Objectives: This course, together with Math 608, covers the fundamental theorems and
examples of graduate Real Analysis: measure theory, analysis on topological spaces, and (in Math
608) basic results from Functional Analysis, and the study of Lp
spaces. These are the topics
whose knowledge is tested on the Real Analysis qualifying exam. The course also provides the
background for further study and research in various fields of Mathematical Analysis, including
Functional and Harmonic Analysis, Banach spaces, Operator Algebras and Operator Theory, and
Brief course outline:
· Abstract measure theory (weeks 13).
-algebras. Measures. Outer measures and Caratheodory's construction.