20324 Measure Theory 1

Credits: 6 advanced credits in Mathematics

Prerequisites: Students must fulfill all English requirements and take bibliographic instruction in the Library.

Required: Infinitesimal Calculus I, Infinitesimal Calculus II, as well as having accumulated at least 36 credits in Mathematics

Recommended: Linear Algebra I

Author: Eli Levin (The previous edition of the course was based on lecture notes by Amnon Jakimovski, and adapted by Dov Monderer, with Daniela Leibowitz, Zippy Berger, Naomi Shaked-Monderer and Shmuel Berger)

Topics: Preparatory section – concepts in set theory, properties of the real line; Algebras and -algebras; Measure spaces; Lebesgue’s outer measure; Lebesgue’s measure; Measurable functions; Almost everywhere and almost uniform convergence; Integrals of simple functions with finite supports; Integrals of measurable functions; The relationship between differentiation and Lebesgue’s integration.

This is a year-long course, however, capable students may increase the pace and complete the course work by the end of the fall semester, or begin later, at any time prior to the beginning of the spring semester.

1A short non-credit seminar may be added to this course. See note under Mathematics seminars.