Graduate Student Colloquium: Jillian Cervantes

The Axiom of Choice and Non-Lebesgue Measurable Sets

Jillian Cervantes
Graduate Student
University of Wisconsin-Milwaukee

In this expository talk, we explore an interesting connection between the axiom of choice and the existence of non-Lebesgue measurable subsets of \mathbb{R}. We state the axiom of choice and discuss its meaning and significance before reviewing properties of measures, Lebesgue measure, and Lebesgue measurable sets. The talk concludes with a construction which uses the axiom of choice to prove the existence of non-Lebesgue measurable sets.