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Course Descriptions

16:640:501 - Theory of Functions of a Real Variable I

Daniel Ocone

Text:  

Real Analysis for Graduate Students, by Richard Bass (download for free online from http://bass.math.uconn.edu/real.html)

Prerequisites:

No prerequisites for Math Ph.D. students; permission of instructor otherwise.

Description:

Basic real variable function theory, measure and integration theory prerequisite to pure and applied analysis.

Topics: Riemann and Lebesgue-Stieltjes integration; measure spaces, measurable functions and measure; Lebesgue measure and integration; convergence theorems for integrals; Lusin and Egorov theorems; product measures and Fubini-Tonelli theorem; signed measures, Radon-Nikodym theorem, and Lebesgue's differentiation theorem.

Note:  A Problem Session for 501 will be held on Wednesdays, 10:00am-11:40am in room 425 for the Fall semester.  There is no need to register for the Problem Sessions.


Sections Taught This Semester:

For more information on instructors and sections for Fall 2017, please see our Fall 2017 Teaching Schedule Page

For more information on instructors and sections for this course for other semesters, please see our Teaching Schedule Page


Previous Semesters

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Department of Mathematics

Department of Mathematics
Rutgers University
Hill Center - Busch Campus
110 Frelinghuysen Road
Piscataway, NJ 08854-8019, USA

Phone: +1.848.445.2390
Fax: +1.732.445.5530