Measure Theory and Integration

Explore foundational concepts of modern measure theory that  underpin advanced mathematical topics such as functional analysis, partial differential equations, and Fourier analysis.  Through lectures and exercises, investigate fundamental concepts of Lebesgue measure and integration theory and apply the definitions and properties of Lebesgue measure and measurable sets.  Discussion includes measurable functions, Lebesgue integrals, limit theorems of integrals, the Fubini theorem, and LP space. Using Latex for mathematical writing, hone mathematical proof and writing skills to communicate mathematics effectively and develop rigorous math thinking to prepare for more advanced courses.

This is an alternating years course.

Prerequisites or Prior Knowledge

B36 “Introduction to Real Analysis” is recommended but not required. The following is expected prerequisite knowledge: basic set theory, mathematical logic, the fundamental property of real numbers; familiarity with limit definitions, and how to use these definitions in rigorous proofs of sequences, continuity and differentiation of real-valued functions; properties of a supremum (or least upper bound) and infimum (or greatest lower bound); basic topology including the definitions of open, closed, compact sets in the Euclidean space; basic definitions and properties of Riemann integrals. Please contact the instructor at the beginning of the course with questions.