In 1946 Mark Kac proved that for a centred Hoelder continuous function $f$ defined on $[0,1]$ and extended periodically to the whole real line, the sequence $f(2^k t)$ satisfies a Central Limit Theorem. We extend the result to measurable $L^2$ functions satisfying a fast approximation property. The result naturally extends to similar functions defined on Bernoulli shifts.

Joint work with Emma Hovhannisyan and Ashkan Nikeghbali (both from the University of Zurich).