Real Analysis 2

Spring 2018


Lecture Office hour Problem session
Wednesday – Thursday
10:00 am – 12:00 pm
11:00 am – 12:00 pm
11:00 am – 12:00 pm


In this course we study the modern techniques of Real Analysis, from measure theory to the basics of functional analysis, as well as applications to Fourier Analysis.



Homeworks & remarks

Real Analysis 2, 2018


DM Bressoud, A radical approach to Lebesgue’s theory of integration, Cambridge, 2008
S Igari, Real analysis with an introduction to wavelet theory, AMS 1998
GB Folland, Real analysis: modern techniques and their applications, Wiley & Sons, 1999
J Franks, A (terse) introduction to Lebesgue integration, AMS, 2009
DA Salamon, Measure and integration, EMS, 2016
B Simon, A comprehensive course in Analysis, Part 1: Real Analysis, AMS 2015
B Simon, A comprehensive course in Analysis, Part 3: Harmonic Analysis, AMS 2015
B Simon, A comprehensive course in Analysis, Part 4: Operator Theory, AMS 2015
EM Stein & R Shakarchi, Real Analysis: measure theory, integration, and hilbert spaces, Princeton, 2005
EM Stein & R Shakarchi, Functional analysis: introduction to further topics in analysis, Princeton, 2011
ME Taylor, Measure theory and integration, AMS, 2006

Midterm evaluations

There will be two midterm evaluations, each with (optional) homework and a written examination.

Homework (40%)

Problems will be assigned weekly and must be submitted each Friday by 11:00 am.

Written exam (60%)

A written one-hour exam will evaluate the material of the course, focusing on the previous 8 weeks.


  • First midterm: April 20
  • Second midterm: June 8

Final evaluation

The final evaluation will consist of a final project and a final written examination.

Project (50%)

Each student will be assigned a final project, extending the results from class. A report must be submitted before the written examination.

Exam (50%)

A two-hour written examination, evaluating the material of the course.


June 27, 10:00 am

Additional examinations

  • Extra: July 4, 10:00 am
  • Regularization: August 8, 10:00 am