Lecturer

Prof. Boris Tsirelson (School of Mathematical Sciences).

Instructor

Yonatan Shelah.

Prerequisites

Analysis 2.

Grading policy

The final exam (07.02; 04.09).

LECTURE NOTES

1. Introduction.
2. The Lebesgue measure.
3. Measurable map, pushforward measure.
4. Integral.
5. Modes of convergence.
6. Iterated integral, product measure.
7. Approximation.
8. Relation to the Riemann integral.
9. Radon-Nikodym theorem and conditioning.

Thanks to Menachem Mostowicz for noticing my mistakes.

TEXTBOOKS

• Terence TAO, "An introduction to measure theory" (AMS, 2011).   Available online.
• Frank JONES, "Lebesgue integration on Euclidean space" (Jones and Bartlett, 1993).
• Marek CAPINSKI and Ekkehard KOPP, "Measure, integral and probability" (Springer 2004).

ADDITIONAL LITERATURE

• Ariel Yadin, "Measure theory" (course, BGU 2015).   Available online; find Lecture Notes there.
• Jeff Viaclovsky, "Measure and integration" (course, MIT 2003).   Available online; find Lecture notes there.
• Elias M. STEIN and Rami SHAKARCHI, "Real analysis: Measure theory, integration, and Hilbert spaces" (Princeton, 2005).
• Brian S. THOMSON, "Theory of the integral" (ClassicalRealAnalysis.com, 2013).   Available online.

EXAMS (in Hebrew)

• 2016, sample
• 07.02.2016; see also typical errors, comments etc.
• 04.09.2016