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Course Descriptions

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

Daniel Ocone


Real Analysis for Graduate Students, by Richard Bass (download for free online from


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


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.

Schedule of Sections:

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