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

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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 approximation to numerical integration*, Diophantine Approximation and its Applications (C. F. Osgood, ed.), Academic Press, New York, 1973, pp. 129-199. MR**0357357 (50:9825)****[2]**I. M. Sobol,*Multidimensional quadrature formulae and Haar functions*, Nauka, Moscow, 1969. MR**0422968 (54:10952)****[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.

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

Article copyright:
© Copyright 1985
American Mathematical Society