Almost sure equidistribution in expansive families

摘要

In this paper we study generic equidistribution in families of sequences ofpoints on tori. Weassume that the sequences are parameterized by some subset of a Euclidean space, and we formulate geometric conditions on the dependence so that equidistribution holds almost everywhere with respect to the Lebesgue measure on the parameter space. As a consequence, we can give a new proof ofan old result by Koksma.