Measure and Integration
A graduate-level MIT OpenCourseWare course covering Lebesgue's measure and integration theory. Topics include construction of Lebesgue measure, measurable functions, convergence theorems (monotone and dominated convergence), Lp spaces, product measures and Fubini's theorem, and an introduction to convolution and the Fourier transform. The course builds the analytical foundations used throughout modern analysis and probability theory, moving from Riemann integration's limitations to a rigorous treatment of integration that handles a much broader class of functions. Materials include lecture notes, problem sets with solutions, and exam materials, following MIT's standard OpenCourseWare format. No enrollment or certificate is offered since OCW is a self-paced archive of course materials rather than an instructor-led class, but all readings and assignments are available at no cost for independent study.