File Name: measure theory and integration lecture notes .zip
Other information, such as learning outcomes, teachers, literature, lecture notes and examination information, are in a separate course PM. Information for first day of course. Presentation slides for Chapter 3 of lecture notes presentationschapter3. Presentation slides for Chapter 4 of lecture notes presentationschapter4.
Today we discussed the simplest nontrivial case of measuring the size of something: the length of a subset of R. Some subsets, like closed or open intervals, are easy to assign length to. Even when we removed a few points from an interval it was easy to assign a length. But then we turned to a harder example: what's the length of the set of all rationals between 0 and 1? Our initial intuition was that it should be 0, because there are far fewer rationals than irrationals. On the other hand, rationals are dense in R , so they still seem to occupy a large proportion of the unit interval.
When approaching measure theory for the first time, the ideas can seem opaque and unmotivated. This is amplified since many students of measure theory are not coming from a strictly mathematics background and may be approaching the material on their own outside of the classroom. In addition to first-year math graduate students and advanced math undergraduates, students in stats, economics, the hard sciences, etc. This is a guide to resources for learning measure theory that tries to keep in mind that many myself included approach the material with an atypical background. Francis Su provides an excellent set of video lectures to get one up to speed on real analysis.
Lecture Notes on Measure Theory and Integration. 2 — Measures. Joel Feldman. University of British Columbia. October 10, 1.
This set of notes was mainly written in while the author was an undergraduate at Imperial College, University of London.
The material covered in these notes is essentially the development of the theory of measure and integration; the lack of time means that there is little in the way of applications of the theory and thus little motivation for the student. I would hope that the material presented in the appendices will show the wide range of applications of the theory. There is one further appendix dealing with applications to number theory and in particular rational approximations to irrationals. Number Theory Back to top. Number Theory.
Autism Independence are bringing together organisations, service users and people interested in helping them meet the needs of young people with autism and their families in the Bristol area. Search list by name The switching principle is shown in Fig. If you do not receive an email within 10 minutes, your email address may not be registered, It connects a broad range of ideas and techniques, from analysis, probability theory, and representation theory to recent applications in number theory. The most important reason for omitting the measure theory is that the intricacies of its development are not needed for its exploitation.
He used Professor Viaclovsky's handwritten notes in producing them. Don't show me this again. This is one of over 2, courses on OCW.
Folland, Gerald B. Real analysis: modern techniques and their applications. Royden, Halsey Lawrence, and Patrick Fitzpatrick. Real analysis.
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