Fourier Analysis and Lebesgue Integration

This is the webpage for the course MATH31011/MATH41011/MATH61011 Fourier Analysis and Lebesgue Integration.

Course Notes

Chapter 1 and (non-examinable) appendix
Chapter 2
Chapter 3 and (non-examinable) appendix
Chapter 4 and (non-examinable) appendix
Extra reading material for 41011/61011 (covers the construction of Lebesgue measure and the existence of non-measurable sets); solutions to exercises 1-8, solutions to exercises 9-16

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Example Sheets

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Past Examination and Feedback

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Books

Buying a book is not essential: everything will be covered in the course notes. The book by Franks is the main recommendation and covers all of the course except for the material on Fourier series in Chapter 1. The book by Bear gives an alternative viewpoint.

J. Franks, A (Terse) Introduction to Lebesgue Integration, American Mathematical Society, Student Mathematical Library, 2009.
H. S. Bear, A Primer of Lebesgue Integration, Academic Press, 1995.

The book by Franks is a bit pricey (around 30 pounds) but the author has posted a draft version, which covers most of it, on the arXiv preprint server at http://uk.arxiv.org/pdf/0802.4076.pdf. Unfortunately, this version doesn't include Chapter 6 of the book, which covers material in the course.

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