Sentence examples for a subsequence of weakly from inspiring English sources

Let be a subsequence of weakly convergent to, then by Step 7 as.

Since is weakly compact, there is a subsequence of converging weakly to some.

Since, also converges to Since, and are continuous, we have Thus   (ii) Proof follows from (i).   (iii) Since is weakly compact, there is a subsequence of converging weakly to some.

Then a subsequence of converges weakly to.

Suppose that a subsequence of converges weakly to.

Now assume that is a weak limit point of and a subsequence of converges weakly to.

The weak compactness of implies that there is a subsequence of converging weakly to as.

So, we assume that a subsequence of converges weakly to We shall show that.

Since is bounded, we can choose a subsequence of converging weakly to.

If follows from reflexivity of and the boundedness of a sequence that there exists which is a subsequence of converging weakly to as.

From Theorem 2.4, for each, there exists such that The weak compactness of implies that there is a subsequence of converging weakly to as.