Generalization of two results of the theory of uniform distribution

Author:
Petko D. Proĭnov

Journal:
Proc. Amer. Math. Soc. **95** (1985), 527-532

MSC:
Primary 11K38

DOI:
https://doi.org/10.1090/S0002-9939-1985-0810157-8

MathSciNet review:
810157

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a sequence of points in and a sequence of nonnegative numbers, define the distribution function

**1**] for the discrepancy of the sequence . Applying the above inequality we also obtain a new criterion for uniform distribution modulo one.

**[1]**H. Niederreiter,*Application of Diophantine approximations to numerical integration*, Diophantine approximation and its applications (Proc. Conf., Washington, D.C., 1972) Academic Press, New York, 1973, pp. 129–199. MR**0357357****[2]**I. M. Tsobol′,*\cyr Mnogomernye kvadraturnye formuly i funktsii Khaara.*, Izdat. “Nauka”, Moscow, 1969 (Russian). MR**0422968****[3]**P. D. Proinov,*Note on the convergence of the general quadrature process with positive weights*, Constructive Function Theory'77 (Bl. Sendov and D. Vačov, eds.), Sofia, 1980, pp. 121-125.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
11K38

Retrieve articles in all journals with MSC: 11K38

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0810157-8

Article copyright:
© Copyright 1985
American Mathematical Society