Graduate Groups and Dynamics Seminar
Samuel Dodds
UIC
Ruiziewicz problem on the sphere
Abstract: The Ruziewicz (a.k.a Banach-Ruziewicz) problem on the $n$-sphere $S^n$ is the question whether the
Lebesgue measure is the unique rotation invariant normalized mean on the Lebesgue
sigma-algebra of the sphere. Here a mean is a finitely additive probability measure.
For $n=1,2$ the answer is negative; for $n\ge 5$ it is positive as was proved independently by
Margulis and Sullivan. For $n=2,3$ the positive answer was proven by Driendfeld.
In the talk the connection between the problem and an existence of a group $G
Tuesday September 18, 2018 at 3:00 PM in 1227 SEO