Sentence examples for an increasing sequence in from inspiring English sources

where is an increasing sequence in such that and.

Indeed, assume that ( ( x n ) ) n ∈ N is an increasing sequence in ( X, ≤ p ).

Thus, there exists an increasing sequence in converging to such that is an open cover of.

Let be the sequence defined by (1.15), where is a sequence in and is an increasing sequence in.

Let { x n } be the sequence defined by (2.7), { α n } is a sequence in ( 0, 1 ) and let { t n } be an increasing sequence in [ 0, ∞ ).

Since ({a_{n}}) is an increasing sequence in A and (a_{n}to a), by hypothesis (iv), (a_{n}preceq a), ∀n.

if ({x_{n}}) is a increasing sequence in A with (x_{n}to xin A) as (ntoinfty), then (x_{n}preceq x) for all (ninmathbb{N}).

Therefore { W k } k = 1 ∞ is an increasing sequence of uniformly bounded convex sets in K.

(b)if an increasing sequence converges to in, then for all ; (v there exists a comparison function such that (3.7).

Following this way, we obtain an increasing sequence ((m_{k})) in (mathbb{N}) and the sequence (a=(a_{k})in c_{0}(widehat{F})) such that begin{aligned} sum_{k=1}^{infty }widehat{F}(a_{k} g(x_{k})= infty.

Let ({C_{1}, C_{2}, ldots}) be an increasing sequence set in advance, such that (|X_{k}(h)|le C_{k}) for all h with probability 1.