English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We prove that a Banach space X has nontrivial cotype if and only if given any a-field X and any sequence tn,,:X -E X of strongly additive vector measures such that for some y > 1 lim supP,, I Iilin(E)iI 0 there exists a positive integer m such that given xl, ... , xm E X, 11xill > 1 for each i = 1, ... m, there exists F C {1, ..., m} such that ZEiEF Xil > C. The payoff: given a sequence (ji,2) of strongly additive X-valued vector measures defined on a v-field X such that there exists a constant y > 1 so that for each E E X lim supn,,0 IbIu/t(E)I I 2) if there is a constant Kq > 0 such that for each n > 1, xl, ..., x, E X, we have ( IlIXkIlq) < Kq Z; rk(t)Xk dt where (rn) denotes the Rademacher sequence on [0, 1]. Received by the editors February 20, 1991; presented at the Special Event in Analysis, Lehigh University, December 14, 1990. 1991 Mathematics Subject Classification. Primary 46B 10, 46B20.

Saeki’s improvement of the Vitali-Hahn-Saks-Nikodým theorem holds precisely for Banach spaces having cotype