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[PAST EVENT] Mathematics Colloquium
April 29, 2011
3pm - 4pm
Title: Well-ordered sets, Ulam matrices, and probability measures
Abstract: This will be a talk about some classical mathematics that I have used throughout my career. Topics will include: the uncountable well-ordered set $\Omega$ and its closed, unbounded subsets; Rudin's theorem on stationary sets in $\Omega$; topological classifi cation of stationary sets; Ulam matrices of subsets of $\Omega$ and Ulam's application to the existence of a non-atomic probability measure on $\Omega$ for which every set is measurable; application to the existence of non-measurable subsets of [0, 1]. Although these topics are rarely mentioned in undergraduate courses, most of the talk will be understandable to students who have taken Math 311.
Abstract: This will be a talk about some classical mathematics that I have used throughout my career. Topics will include: the uncountable well-ordered set $\Omega$ and its closed, unbounded subsets; Rudin's theorem on stationary sets in $\Omega$; topological classifi cation of stationary sets; Ulam matrices of subsets of $\Omega$ and Ulam's application to the existence of a non-atomic probability measure on $\Omega$ for which every set is measurable; application to the existence of non-measurable subsets of [0, 1]. Although these topics are rarely mentioned in undergraduate courses, most of the talk will be understandable to students who have taken Math 311.