This is the course website for the ICTP course Real Analysis for diploma students during the first semester of 2025.
After taking the course, students will be familiar with the Lebesgue measure and the Lebesgue integral and their basic properties.
We follow the text books
E. M. Stein and R. Shakarchi, Real analysis. Measure theory, integration, and Hilbert spaces. Princeton, NJ: Princeton University Press (2005; Zbl 1081.28001)
and
L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions. Revised ed. Boca Raton, FL: CRC Press (2015; Zbl 1310.28001)
Other inspiration sources are
the Real Analysis lectures by Emanuel Carneiro at ICTP, and
the lecture notes by Juha Kinnunen at Aalto University on measure and integral and
Please read the corresponding sections of the lecture notes before the lecture.
We will not cover every detail of the material during the lectures but instead have more interactive sessions during which we focus on the more difficult parts and try to gain a more general understanding of the material.
After having read the material you can test your knowledge by trying to answer the questions from the corresponding quiz.
Please hand in the exercises before the exercise session.