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Almost Convergence and Well-Distributed Sequences

Published online by Cambridge University Press:  20 November 2018

Alan Zame
Alan Zame*
Affiliation:
University of Miami, Coral Gables, Florida
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A sequence (xn) of real numbers is said to be well-distributed modulo 1 (abbreviated w.d.) if for each subinterval I = [a, b] of [0, 1] we have that

where χI is the characteristic function of I modulo 1. A sequence (r n ) of positive numbers is lacunary if

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 1211 - 1214
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Koksma, J. F., Ein mengentheoretischer Satz tiber die Gleichverteilung mod Eins, Compositio Math. 2 (1935), 250–258.Google Scholar
2. Petersen, G. M., Almost convergence and uniformly distributed sequences, Quart. J. Math. Oxford Ser. 7 (1956), 188–191.Google Scholar
3. Petersen, G. M., On the structure of well-distributed sequences. V, Indag. Math. 29 (1967), 229–233.Google Scholar
4. Zame, A., The measure of well-distributed sequences, Proc. Amer. Math. Soc. 18 (1967), 575–579.Google Scholar