Sentence examples for be two sequences such from inspiring English sources

Let (p=(p_{n})) and (q=(q_{n})) be two sequences such that (0< p_{n}, q_{n}<1), and let (p_{n}rightarrow1) and (q_{n}rightarrow1) as (nrightarrow infty).

Let x = ( x k ) and y = ( y k ) be two sequences such that x k − L 1 = C 1 ( s t ) - o ( a n ) and y k − L 2 = C 1 ( s t ) - o ( b n ).

Assume that ({a_{n}},{b_{n}}subset ( 0,infty ) cap A) are two sequences such that ({b_{n}}rightarrow0) and (varrho(a_{n},b_{n})>0) for all (ninmathbb{N}).

If ({a_{n}},{b_{n}}subset ( 0,infty ) cap A) are two sequences such that ({b_{n}} rightarrow0) and (varrho(a_{n},b_{n})>0) for all (ninmathbb{N}), then ({a_{n}}rightarrow0). Notice that conditions ((varrho_{1})), ((varrho_{2})) and ((varrho_{3})) establish that if there exist sequences verifying some assumptions, then a thesis must hold.

(d) demiclosed random operator (at y) if {x n } and {y n } are two sequences such that T ω, x n ) = y n and {x n } converges weakly to x and {T ω, x n )} converges to y imply that x ∈ F and T ω, x) = y, for each ω ∈ Ω.  .

In fact, if ((t_{n})_{n}) and ((s_{n})_{n}) are two sequences such that (vert t_{n}-s_{n} vert to0), then from the uniform continuity of (sigma (cdot)) (Lemma 6) we have biglvert bigl(t_{n}-sigma (t_{n}) bigr)- bigl(s_{n}-sigma (s_{n}) bigr) bigrvert leq vert t_{n}-s_{n} vert + biglvert sigma (t_{n} -sigma (s_{n}) bigrvert_{n} -sigmaoinfty).

If ( x j ), ( y j ) and ( z j ) are three sequences such that (i) x j ≤ y j ≤ z j, for all j ∈ N,   (ii) S θ - lim j x j = ξ = S θ - lim j z j,  .

If ( x j ), ( y j ) and ( z j ) are three sequences such that (i) x j ≤ y j ≤ z j for all j ∈ N,   (ii) S λ - lim j x j = ξ = S λ - lim j z j,  .

Let and be two sequences in such that.

Let be a uniformly convex and smooth Banach space and let and be two sequences in such that either or is bounded.

Let be a uniformly convex and smooth Banach space and let, be two sequences of such that either or is bounded.