Syllabus/achievement requirements

The primary literature for this course is the book "A Course in Real Analysis" by John N. McDonald and Neil A. Weiss, Second edition, Academic Press, ISBN 978-0-12-387774-1. Hereafter and in the timeplan I will use the abbreviation [MW] to refer to this book.

As supplementary or alternative reading material I recommend the new book "Topics in Real and Functional Analysis" by Gerald Teschl. You can get a copy of the book at the author's webpage. 

The plan is to cover material in the following sections, though not necessarily in this order, from [MW]: sections 6.2 to 6.4, sections 7.1 to 7.3, sections 9.1 to 9.4, section 12.1, sections 13.4 to 13.6, sections 14.1 to 14.3. Time permitting, also some parts in sections 15.1 to 15.5.

Updated 21 November 2018: sections 6.2, 6.3 (including the monotone class lemma from section 1.4), 6.4 (up until and including Example 6.12),  7.1, 7.2 (up until and including Theorem 7.2), 7.3 (essentially only Def. 7.11), 9.1, 9.2 (except Prop. 9.2), 9.3, 12.1, 13.4 (The dual of L^p), 13.5, 13.6, 14.1, 14.2. All this material is relevant for the exam. We also covered parts of Section 15.1 (up to Prop. 15.2) and 15.3 (parts of Thm 15.5, Thm 15.8 for smooth functions with compact support, Prop 15.4 and Thm 15.9(a)), however this material will not be required for the exam.