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Graduate Seminar

Andrew Zucker
Carnegie Mellon University
Title: A descriptive proof of the pointwise ergodic theorem

Abstract: The pointwise ergodic theorem is one of the most important results in ergodic theory: If $f$ is an $L^1$ function on a standard probability space $(X, \mu)$ and $T: X \to X$ is an invertible $\mu$-preserving transformation, then the averages of $f$ converge pointwise a.e. to the expectation of $f$. Analysis proofs of this result are rather difficult, and typically go by proving some sort of maximal inequality. Instead of maximal inequality, we proceed via minimal effort! Anush Tserunyan has recently found a super slick proof of the pointwise ergodic theorem using only some basic descriptive set theory. In this talk, we will discuss the necessary descriptive set theory background and give Tserunyan's proof.

Date: Tuesday, April 11, 2017
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Yangxi Ou
Note: Video on YouTube: