2002 Fall MATH 241-01
Bulletin Course Description Measures; Lebesgue integral; Lk spaces; Daniell integral, differentiation theory, product measures. Instructor: Staff
(Instructor named in bulletin description above may not be current. For current instructor, see listing below.)
Title REAL ANALYSIS I Department MATH Course Number 2002 Fall 241 Section Number 01 Primary Instructor Huber,Mark Lawrence Prerequisites Prerequisite: Mathematics 204 or equivalent. Course Homepage https://courses.duke.edu
Prerequisites
An undergraduate course in real analysis, such as Math 204 at Duke.
Synopsis of course content
This is a course in measure theory. The idea of measure is the foundation of a modern understanding of integration and probability, and in this course we build this foundation from the ground up. We'll begin with a simple example of a measure, Lebesgue measure, and work our way up to more sophisticated examples. Some of the major theorems we'll look at include the monotone convergence theorem, the dominated convergence theorem, Fubini's Theorem, and the Radon-Nikodym theorem.
Textbooks
H. L. Royden, "Real Analysis, Third Edition", Prentice Hall
Assignments
Weekly--some applications but mostly proofs.
Exams
Two short (30 minutes at most) exams testing basic knowledge of definitions and statements of theorems.
Term Papers
none
Grade to be based on
Written work
