Dan Mauldin : Ergodic theory and homeomorphic Bernoulli trial measures on the Cantor space

Posted by , part of the Departmental Colloquium.

At

Oct. 31, 2008, 3 p.m.

In

SEO 636

Abstract

The following problem has its origins in some early work of Ulam and Oxtoby in the foundations of ergodic theory. For each r, 0< r <1, let m(r) be the measure on the Cantor space induced by an infinite sequence of independent Bernoulli trials. The question is: given m(r) and m(s), when is there a homeomorphism, h, of Cantor space such that m(r)(E) = m(s)(h(E)), for each Borel set E. We will answer this question and will pose a number of related still unsolved questions