"Tiger gotta hunt. Bird gotta fly.
Man gotta sit and wonder why, why, why.
Tiger gotta sleep. Bird gotta land.
Man gotta tell himself he understand."
Kurt Vonnegut Jr.


Math 5331: Real Analysis-Measure Theory

 

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  • Instructor: M. A. Khamsi.
  • Phone: 747-6763,
  • Office hours: TTH 12:00-1:00PM in BH 328, or by appointment
  • Meeting Time/Place: MW 3:00PM-4:20PM 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 functional-Analytic 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 self-contained 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)


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