Math 617
Instructor: Clayton Shonkwiler
Time: Monday, Wednesday, Friday, 3:00–4:00
Location: Engineering E205
Office: Weber 206C
Office Hours: By appointment
Email Address: clayton.shonkwiler@colostate.edu
Text: Measure, Integration & Real Analysis, by Sheldon Axler
Syllabus
Overview
Measure theory provides the theoretical underpinnings of modern definitions of the integral and serves as the foundation for current approaches to functional analysis and distribution theory – and hence in particular to solving partial differential equations – as well as to probability theory, fractals, and dynamical systems.
The main goal of the course is to develop the basic theory: definitions and examples of \(\sigma\)-algebras and measures, the definition of measurable functions and of the Lebesgue integral, and the Lebesgue–Radon–Nikodym theorem. That groundwork will then allow us to develop applications of the theory to probability.
A background in classical real analysis (i.e., MATH 517 material) and some familiarity with the basic concepts of point-set topology and vector spaces are essential prerequisites.
The following books may be useful additional resources:
- Topics in Real Analysis, by Gerald Teschl
- An Introduction to Measure Theory, by Terence Tao
- Real Analysis: Measure Theory, Integration, and Hilbert Spaces, by Elias M. Stein and Rami Shakarchi
- Real Analysis: Modern Techniques and Their Applications, by Gerald B. Folland
Readings and homework will be assigned through Canvas.