Price and Haar Type Functions and Uniform Distribution of Sequences

摘要

The Weyl criterion is shown in the terms of Price functions and Haar type functions. We define the so-called modified integrals of Price and Haar type functions and obtain the analogues of the criterion of Weyl, the inequalities of LeVeque and Erdos-Turan and the formula of Koksma in the terms of the modified integrals of Price and Haar type functions.