International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 4, Pages 775-777

Almost none of the sequences of 0's and 1's are almost convergent

Jeff Connor

Department of Mathematics, Ohio University, Athens 45701, Ohio, USA

Received 21 July 1989; Revised 5 February 1990

Copyright © 1990 Jeff Connor. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We establish that, in the sense of the Law of Large Numbers, almost none of the sequences of 0’s and 1’s are assigned the same value by every Banach limit.