- The final exam is on Thursday, December 10, 8:30 am, in BUCH B209.
- Homework #1 was due on Friday, September 25. Homework #1 solutions
- Homework #2 was due on Friday, October 9 Homework #2 solutions
- Homework #3 was due on Friday, October 23. Homework #3 solutions
- Homework #4 was due on Friday, November 6. Homework #4 solutions
- Homework #5 was due on Friday, November 20. Homework #5 solutions
- Homework #6 is due on Wednesday, December 2.
- We will be skipping some of the material from Chapter 2 of the textbook. The updated syllabus is below.

- Contact information: Math Bldg 200, 604-822-4457, ilaba(at)math.ubc.ca
- Lectures: MWF 9-10, MATH 202
- Office hours: Mon 1-2, Wed 10-11, Fri 11-12, in MATH 200
- The best way to contact the instructor is by email. Please note that email received on evenings and weekends will be answered on the next business day. If you cannot attend regular office hours due to schedule conflict, please make an appointment in advance. Drop-ins and same-day requests for appointments cannot always be accommodated.

This is a cross-listed 4th year undergraduate and graduate course which develops the theory of measure and integration. This material is a cornerstone of mathematical analysis and is an essential part of an advanced mathematical education. It will be used in functional analysis, harmonic analysis, partial differential equations, probability, mathematical physics and information theory. The course will be primarily based on the first 3 chapters of the text:

**Measures (Chapter 1):**sigma-algebras, outer measures, Borel measures on the real line, Lebesgue measure. We covered essentially everything in this chapter.**Integration (Chapter 2):**measurable functions, integration, convergence theorems, product measures and Fubini's theorem.- We covered essentially everything in Sections 2.1-2.5, except that we skipped the gamma function in Section 2.3 (p. 58)
- Section 2.6: we discussed the n-dimensional Lebesgue measure and the relation between Lebesgue and Riemann integration. We skipped the computational part (behaviour of Lebesgue measure under linear transformations, Theorem 2.44, Corollary 2.46 and Theorem 2.47).
- We also skipped Section 2.7, Integration in polar coordinates.

**Differentiation of Measures (Chapter 3):**signed measures, Radon-Nikodym theorem, Hardy-Littlewood differentiation, fundamental theorem of calculus revisited. We will likely be able to cover only the first 2-3 sections. Updates will be posted here.

The final exam will be 2.5 hour long (standard length at UBC). The date of the final examination will be announced by the Registar later in the term. Attendance at the final examination is required, so be careful about making other committments (such as travel) before this date is confirmed. The examination will be strictly closed-book: no formula sheets, calculators, or other aids will be allowed.

[Mathematics Department] [University of British Columbia]