Article PDF
References
Billingsley,P.: Convergence of Probability Measures. New York: Wiley 1968.
Davenport,H., Erdös,P., LeVeque,W.: On Weyl's criterion for uniform distribution. Michigan Math. J. 10, 311–314 (1963).
Hlawka,E.: Ein metrischer Satz in der Theorie der C-Gleichverteilung. Monatsh. Math. 74, 108–118 (1970).
Holewijn,P.J.: On the uniform distribution of sequences of random variables. Z. Wahrscheinlichkeitsth. verw. Gebiete 14, 89–92 (1969).
Kuipers,L., van der Steen, P.: Metric theorems in the theory of asymptotic distribution modulo 1. Indagationes Math. 28, 300–310 (1966).
Loynes,R.M.: On certain applications of the spectral representation of stationary processes. Z. Wahrscheinlichkeitsth. verw. Gebiete 5, 180–186 (1966).
Robbins,H.: On the equidistribution of sums of independent random variables. Proc. Amer. Math. Soc. 4, 786–799 (1953).
Breiman,L.: Probability. Addison Wesley 1968.
Doob,J.L.: Stochastic Processes. New York: Wiley 1953.
Grenander,U.: Probabilities on Algebraic Structures. New York: Wiley 1963.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Loynes, R.M. Some results in the probabilistic theory of asymptotic uniform distribution modulo 1. Z. Wahrscheinlichkeitstheorie verw Gebiete 26, 33–41 (1973). https://doi.org/10.1007/BF00533958
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00533958