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 Instructor: M. A. Khamsi.
 Phone: 7476763,
 Office hours: TTH 12:001:00PM in BH 328, or by appointment
 Meeting Time/Place: MW 3:00PM4:20PM in Classroom Building C202
 Khamsi's Real Analysis page
 Target Audience: Senior Undergraduate Math Majors (as Independent Study), Graduate Students in
Mathematics and Statistics, MAT Students.
 Course Content: This will be your first course on Measure Theory and Integration.
As you might have realized in your Calculus classes, there are severe drawbacks in the usual Riemann Integration studied therein.
For example, it is not possible to integrate functions on sets other than intervals. Likewise,
the integral of the sum of an infinite series is not always the sum of the integrals of the
terms. A more flexible theory of integration (which in some sense, to be made precise in
the course of the semester, contains the Riemann theory) was introduced by H. Lebesgue
in his Doctoral dissertation in 1905.
 The Real Variable course can roughly de divided into three parts: First, we will describe
the sets and the functions that will be involved in the integration process (via Measure Theory).
Secondly the integral will be defined and its properties studied. Finally the functionalAnalytic
implications and several applications (including some to Probability) will be inspected.
 Prerequisite: A good foundation in General Topology, Linear Algebra, and Advanced Analysis.
Some notions on Normed and Metric Space theory will be of invaluable help. However, the class
will be essentially selfcontained and all mathematical objects (beyond those studied in elementary
undergraduate math classes) needed, will be defined on the way.
 Textbook: H.L. Royden,
Real Analysis (Third Edition)
