Sentence examples for sequential limits from inspiring English sources

In [1] Fast introduced an extension of the usual concept of sequential limits which he called statistical convergence.

Denote by ω w ({x n }) the set of weakly sequential limits of the sequence {x n }, that is, ω w ({x n }) = {p : there exists a subsequence of {x n } such that }.

However, the study of the sequential limits ϵ 1 → 0 followed by ϵ 2 → 0 or ϵ 2 → 0 followed by ϵ 1 → 0 can be deduced from an appropriate combination of classical periodic and stochastic averaging theorems:  .

X has the sequential limit comparison property.  .

X has the sequential limit comparison property.

Also, ( X, G ) has the sequential limit comparison property.

It is known that ( X, ⪯ ) has the sequential limit comparison property [37].

Fast [3] extended the usual concept of sequential limit and called it statistical convergence.

The sequential limit comparison property implies that g x n + 1 ⪯ q.

Theorem 2.1 Let ( X, ⪯, G p ) be a partially ordered G p -metric space with the sequential limit comparison property.

The derivation is based on a "sequential limit-analysis" of a hollow sphere made of a rigid-hardenable material.