# Resources for MATH3969: Measure Theory and Fourier Analysis (Advanced)

This page contains links to tutorial and assignment sheets and other handouts (no hard copies will be distributed).

Also look at the Unit Information Sheet.

## What's New

Important announcements will be posted here.

• Solutions to Solutions to Assignment 2 and Quiz 2 are now available.
• Please complete the Unit of Study Survey! Thank you.

• Look at the Exam Information:

Check the official exam information. The time and venue for the exam is available through SydneyStudent.

Pre Exam consultations: Thursday 3 Nov 14:00-16:00, Tuesday 7 November 1-3 pm and Tuesday 14 Nov 2-4 pm, or by appointment. You can also ask questions on Ed.

Only material covered in lectures and tutorials will be tested. The exam will also contain questions on the theory and proofs, and not just problems to solve. In particular there will be a question on properties of conditional expectation and other properties relating to probability measures.

You can look at the exams from 2009, 2011, 2012, 2013, 2014 and their solutions: 2009, 2011, no solutions for 2012, 2013, 2014

Note that all rules regarding special consideration apply.

• The second assignment is out now. It is due on 30 October.
• Quiz 2 takes place Tuesday 17 October 9–10am in New Law 440 (the tutorial room).

If for some exceptional reason you are unable to do the quiz at that time please email me immediately at MATH3969@maths.usyd.edu.au with your name and SID by Friday 13 October 12pm.

The material covered is Sections 9–31:

• Measurable functions, abstract integration
• limit theorems (monotone/dominated convergence, continuity and differentiability of integrals)
• Theory of $$L^p$$-spaces (main properties, Hölder, Jensen , Minkowski inequality)
• Theory and application of convolution and approximate identities
• Definition and basic properties of Fourier Transform.

Tested will be the understanding of definitions and, the main theorems and the ability to apply and verify these in simple examples.

You can look at the quizzes from 2011, 2012, 2014, 2015 and their solutions 2011, 2012, 2014, 2015 to get an idea of the style and degree of difficulty.

Note that all rules regarding special consideration apply.

• The first assingment has been returned through the LMS. Solutions to Assignment 1 are available. You can check your mark from the MATH3969 page.

• Solutions to Quiz 1 are available. The quiz is returned in the lecture 4 October. Those who did not collect it can obtain it from the lecturer in Carslaw Room 715. You can check your mark from the MATH3969 page. Some feedback is included in the solutions.

• The first assignment is out now. It is due on 11 September.
• You might want to participate in the inaugural Simon Marais Mathematics Competition. If you are interested please contact Milena Radnovic before Friday 15 September.
• Make use of the Ed Discussion Forum to ask questions or share course related material.
• Quiz 1 takes place Tuesday 22 August 9-10am in New Law 440 (the tutorial room).

If for some exceptional reason you are unable to do the quiz at that time please email me immediately at MATH3969@maths.usyd.edu.au with your name and SID by Thursday 17 August.

Material covered is Sections 1–5 and part of 8 in the lecture notes, as well as examples and techniques from tutorials. In Section 8 only Propostion 8.1 is covered (was part of tutorials). Outcomes (from Unit Information Sheet) covered are: Student

• is familiar with the basics of abstract measure and integration theory;
• has a good idea on the construction of measures from outer measures with application to the Lebesgue measure and related measures;
• is able to find and write simple proofs, and apply the theory in a number of applications.

You can look at the quizzes from 2011, 2012, 2014, 2015, 2016 and their solutions 2011, 2012, 2014, 2015, 2016 to get an idea of the style and degree of difficulty. (Some of these quizzes cover more material than required this year)

Note that all rules regarding special consideration apply.

• If you have not done MATH2962 or MATH3961 you need to catch up on some topological concepts. Please read Analysis Revisions, particularly the first part on supremums and infimums.

## Schedule

Tutorial and assignment sheets and solutions are available as PDF files. If you have problems printing the PDF files look at the PDF Help Page

Tutorials (PDF) Assessments due Other handouts Lectures/Material covered
Week 1 No Tutorials   Analysis Revisions Lectures Week 1
Week 2 Tutorial 1 / Solutions     Lectures Week 2
Week 3 Tutorial 2 / Solutions     Lectures Week 3
Week 4 Tutorial 3 / Solutions Quiz 1, 22 August   Lectures Week 4
Week 5 Tutorial 4 / Solutions     Lectures Week 5
Week 6 Tutorial 5 / Solutions     Lectures Week 6
Week 7 Tutorial 6 / Solutions Assignment 1, 11 September   Lectures Week 7
Week 8 Tutorial 7 / Solutions     Lectures Week 8
Semester break
Week 9 Tutorial 8 / Solutions     Lectures Week 9
Week 10 Tutorial 9 / Solutions     Lectures Week 10
Week 11 Tutorial 10 / Solutions Quiz 2, 17 October   Lectures Week 11
Week 12 Tutorial 11 / Solutions     Lectures Week 12
Week 13 Tutorial 12 / Solutions Assignment 2, 30 October   Lectures Week 13