Special topics course offered in Fall 2022 and Fall 2021 by Christopher Heil.
This course can be taken in place of MATH 6337, Real Analysis, to satisfy the prerequisite for MATH 6241, Probability I.
This course cannot be used for credit at the same time as MATH 6337
Online lecture notes
Lebesgue measure and integral, abstract measure theory,
focused on "applicable" topics.
Review of background.
Exterior measure and Lebesgue measure on the real line.
Lebesgue integration on the real line: measurable functions, convergence in measure, Lebesgue integral, Monotone Convergence Theorem, Fatou's Lemma, Dominated Convergence Theorem, Fubini's Theorem.
Abstract measure theory, including:
- Sigma-algebras and measurability.
- Outer measures and premeasures.
- Integration and convergence theorems.
- Radon--Nikodym Theorem.
- Caratheodory Extension Theorem.