Christian Rosendal : Christensen's problem on automatic continuity of universally measurable homomorphisms. (continued)

Posted by , part of the Logic Seminar.

At

Feb. 17, 2009, 4 p.m.

In

SEO 612

Abstract

An old problem due to Christensen asks whether any universally measurable homomorphism (i.e., measurable with respect to any Borel probability measure) between Polish (i.e. separable, complete metric) groups is continuous. This was originally settled for the group of real numbers by Steinhaus and later for any second countable locally compact group by Weil in the first half of the 20th century. However, since locally compact groups are exactly those that admit translation invariant measures, the situation for arbitrary Polish groups is radically different. Nevertheless, Steinhaus and Weil's result was extended to Abelian groups by Christensen in the late 1960s via his notion of Haar null sets in arbitrary Polish groups and subsequent work mainly by Solecki has further extended this to larger classes of Polish groups. I will give an introduction to the basic theory and also present some new results pointing towards a positive answer to Christensen's problem.

seminar begins with tea.