Abstract
A Weyl criterion using Walsh functions is established and the relation between uniform distribution mod 1 and dyadic addition on the real line is investigated. Further, we develop the relationship between the modified integrals of the Walsh func-tions and uniform distribution mod1:a "Walsh integrals" Weyl criterion is developed and analogues of the LeVeque inequality and the Erdös-Turán inequality are obtained. These bounds are easier to compute than the classical bounds.
