Math 6320, Introduction to Real Analysis 2
Semester 2, 2019-20
Dr. Judith Packer, Dept. of Mathematics
Tel: (303) 492-6979
Office: Math 227
This course is meant to continue the study of analysis of real-valued functions of one or several variables,
with an emphasis on Lebesgue measure
and Lebesgue integration on the real line and R^n.
Topics to be covered include:
Locally compact Hausdorff spaces, the Stone-Weierstrass Theorem, the Arzela-Ascoli Theorem;
Elements of functional analysis, including normed
vector spaces, linear functionals, the Baire Category Theorem;
Measure and integration: general theory, signed measures - the Hahn and Jordan decomposition
theorem, outer measures and Caratheodory's extension theorem,
the Radon-Nikodym Theorem; General L^p spaces and duality;
Product measures, the Fubini and Tonelli Theorems, cumulative distribution theorems and
Borel measures on R;
Radon measures: positive linear functionals on C_C(X) and the Riesz representation theorems,
regularity of measures, the dual of $C_0(X),$ products of Radon measures;
Elements of Fourier analysis:
convolutions, the Fourier transform, summation of Fourier integrals and series
and appplications of Hilbert space theory, pointwise convergence of Fourier series, Fourier analysis of measures.
Math 6310, or instructor consent.
We will use as a primary text the book
"Real Analysis, 4th Edition, by Halsey Royden and Patrick Fitzpatrick, Pearson, 2010, covering much of Chapters 10, 12, 16,
17, 18, 19, and 20.
Fitzpatrick has an errata page for this textbook at
Lecture Hours and Venue:
- Homework Assignments (every two weeks or so): 30 %
- Midterm test 1 in class - Friday, Feb. 21, 2020, 1 p.m - 1:55 p.m. : 20 %
- Midterm test 2 take-home: given out Monday, March 30, 2020, 1:50 p.m., due Monday April 6, 2020, 1 p.m. : 20 %
- Final exam, Monday, May 4, 2020 in class , 4:30 p.m. - 7 p.m. : 30 % .
- Click HERE for a detailed syllabus of the course, including all university
policies and procedures.
MWF 1 p.m.-1:50 p.m. KCEN N252.
MWF 11-12, and by appointment.
Some Important Names associated with Real Analysis :
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Last modified December 20, 2019.