This is the homepage for MATH 4280 (Measure Theory). This page will be updated throughout the term with information for our course, including homework assignments, review materials, and more. |
Course meets every TR from 2:00 p.m. - 3:50 p.m. in Olin Hall room 103.
Text: Real Analysis: Modern Techniques and Their Applications, 2nd edition, by Gerald Folland.
We will cover introductory aspects of measure theory. In particular, we'll discuss what a measure is, what it can be used for, and how one can construct them. We'll define measurability and integrability of functions from this new viewpoint, and discuss how it yields a more general type of integration for functions from the reals to the reals than classical Riemann integration (namely, Lebesgue integration). This will allow us to revisit various topics you've seen from real analysis (such as convergence theorems, pointwise vs. uniform convergence, Fundamental Theorem of Calculus) in a greater and more useful generality. Depending on how much time remains, we may cover some more advanced topics such as L^p spaces, Fourier analysis, or Haar measures on topological groups.
A running theme throughout the course will be comparing measure-theoretic and topological properties. For instance, we'll discuss and prove Littlewood's so-called three principles of real analysis: any (Lebesgue) measurable set is "almost" a union of intervals, any (Lebesgue) measurable function is "almost" a continuous function, and any series of functions which converge pointwise converge "almost" uniformly.
The prerequisites are some course in topology/metric spaces (MATH 3110/4110 or MATH 3260/4110) and real analysis (MATH 3161). If you are not sure whether you are a good candidate for the class, please feel free to come talk to me.
Your term grade will consist of homework assignments, one midterm exam, and one final exam, broken down in the following way:
You will have one midterm exam on Friday, February 12th (location TBA) and a final exam on Friday, March 11th. The final exam will be in our classroom (Olin 103) during classtime (2:00 p.m. - 3:50 p.m.)