Almost sure equidistribution in expansive families ✩

In this paper we study generic equidistribution in families of sequences of points on tori. We assume 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 of an old result by Koksma.