Sentence examples for contains a subsequence that from inspiring English sources

Thus we prove that for every sequence {gn}n<ω in a locally compact group G, then either {gn}n<ω has a weak Cauchy subsequence or contains a subsequence that is an I0 set.

Furthermore, the sequence ({|u_{lambda_{n}}|}) contains a subsequence that converges to a number η ((0leqetaleq d)).

It is well known that: every bounded sequence contains a subsequence that is regular relative to a given set (see [[16], Lemma 15.2] or [[18], Theorem 1]).

The potential target genes contained a subsequence that had at most d T mismatches (in this case, d T  = 4) with the selected siRNA sense strand.

It follows from and which are bounded and Theorem 2.1 that contains a subsequence, denoted again by, such that (326).

Then X is said to have the Banach-Saks property, if every bounded sequence (u= u_{n})) contains a subsequence (v=(v_{n})) such that the Cesàro means (frac{1}{n+1}^{n}v_{k}^{n}v_{k}) are norm convergent [15].

X is said to have the weak Banach-Saks property, if every weakly null sequence (u= u_{n})) contains a subsequence (v=(v_{n})) such that the Cesàro means (frac{1}{n+1}^{n}v_{k}^{n}v_{k}) are norm convergent [15].

end{aligned} Next, we will show that ({y_{n}}) contains a subsequence converging strongly to (tilde{x}) such that (tilde{x}=P_{F(T }f tilde{x})), which is equivalent to the following variational inequality: bigllangle overrightarrow{tilde{x} f tilde{x})},overrightarrow {xtilde{x}} bigrrangle geq0, quadforall xin F(T).

Since M is inner semicompact at ((hat{x},hat{y})), for the above ((x_{k},y_{k})), there exists a sequence of (z_{k}in M x_{k},y_{k})) that contains a subsequence converging to some ẑ.

Let now be a sequence such that as and let be abbreviated as All we need to prove is that contains a subsequence converging strongly to Since is bounded and since is bounded convex, by passing to a subsequence if necessary, we may assume that converges weakly to a point By Proposition 3.1, we deduce that (3.23).

Then ({u_{k}}) contains a convergent subsequence that is still denoted ({u_{k}} ) for convenience, satisfying u_{k} rightharpoonup u^_{m} quadmbox{weakly in } H_{T},quad mbox{as } krightarrowinfty.