Harry I. Miller

More on the Borwein-Ditor theorem

In 1978 D. Borwein and S. Z. Ditor published a paper answering a question of P. Erdos. Since then several authors including N. Bingham, P. Komjath, H. Miller, L. Miller-Van Wieren, A. Ostaszewski have generalized and extended their result. In this paper a significant generalization of all previous results is presented.

STATISTICAL CLUSTER POINTS OF SUBSEQUENCES OF DOUBLE SEQUENCES

Tha main result of this paper is the double sequence analogue of a theorem about cluster points of single sequences that has recently submitted for publication [8]. Namely, we show here that if x is a double sequence then Γx (the set of statistical cluster points of x) equals Γy (the set of statistical cluster points of y) for “almost all” subsequences y of x.

Some statistical cluster point theorems

In this paper, we present results related to sets of statistical limit points and cluster points of sequences and their matrix transformations, single and double sequences and stretchings of sequences.