MATH 621 Measure Theory
Measure theory provides a foundation for many branches of mathematics, such as harmonic analysis, ergodic theory, theory of partial differential equations and probability theory. It is a central, extremely useful part of modern analysis, and many further interesting generalizations of measure theory have been developed. This course is an introduction to abstract measure theory and the Lebesgue integral. The Lebesgue integral is introduced, and the main convergence theorems are proved. Emphasis is given to the construction of the Lebesgue measure in Rn. Other topics treated in the course are Lp–spaces, the Radon-Nikodym theorem, the Lebesgue differentiation theorem, and the Fubini theorem.
Prerequisite
Undergraduate courses in Linear algebra, real analysis, and topology