A remark on random and equidistributed sequences (Q1202903)

It is known that the average of the values of a function \(f\) on the points of an equidistributed sequence in \([0,1]^ n\) converges to the integral of the Riemann integrable function \(f\). In this paper, three propositions are given, which show that a small random absolutely continuous perturbation of an equidistributed sequence allows to integrate more irregular functions such as bounded Borel functions and bounded quasi-continuous functions.