Almost none of the sequences of 0’s and 1’s are almost convergent. (English) Zbl 0717.40002

Connor, Jeff

Int. J. Math. Math. Sci. 13, No. 4, 775-778 (1990).

Summary: 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.

MSC:

40A05	Convergence and divergence of series and sequences
40A25	Approximation to limiting values (summation of series, etc.)
40G99	Special methods of summability

Keywords:

almost convergence; Banach limit