Logic Seminar
Christian Rosendal
UIC
Christensen's problem on automatic continuity of universally measurable homomorphisms.
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.
Tuesday February 10, 2009 at 4:00 PM in SEO 612