It is known that accumulation points of a pointwise bounded sequence (f n) n of continuous functions on a Polish space are pointwise limits of subsequences if all accumulation points are Borel. Here we present a quantitative variant of this result: For 0 0 and any accumulation point f there is a subsequence (f nk) k with lim sup k jf(x) ? f nk (x)j 0 for… (More)

The possibility of nding small blocks implies the existence of norm convergent subsequences. to appear in "Proceedings of the 1994 Trier conference on Functional Analysis

E Behrends

The possibility of nding small blocks implies the…