Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Saeki’s improvement of the Vitali-Hahn-Saks-Nikodým theorem holds precisely for Banach spaces having cotype
HTML articles powered by AMS MathViewer

by Paul Abraham PDF
Proc. Amer. Math. Soc. 116 (1992), 171-173 Request permission

Abstract:

We prove that a Banach space $X$ has nontrivial cotype if and only if given any $\sigma$-field $\Sigma$ and any sequence ${\mu _n}:\Sigma \to X$ of strongly additive vector measures such that for some $\gamma \geq 1,\lim {\sup _{n \to \infty }}\left \| {{\mu _n}\left ( E \right )} \right \| \leq \gamma \lim {\inf _{n \to \infty }}\left \| {{\mu _n}\left ( E \right )} \right \| < \infty$ for each $E \in \Sigma$ then $\left \{ {{\mu _n}:n \in \mathbb {N}} \right \}$ is uniformly strongly additive.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B20
  • Retrieve articles in all journals with MSC: 46B20
Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 116 (1992), 171-173
  • MSC: Primary 46B20
  • DOI: https://doi.org/10.1090/S0002-9939-1992-1095219-9
  • MathSciNet review: 1095219