Webs and Bounded Finitely Additive Measures

✍ Scribed by Manuel López-Pellicer

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 238 KB
• Volume: 210
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.1997.5401

✦ Synopsis

defined on a -algebra A A. The Nikodym᎐Grothendieck boundedness theorem states that if M is simply bounded in A A then M is uniformly bounded in A A. In this Ä 4 paper we prove that if V V s A A : p, n , n . . . n g ‫ގ‬ is an increasing web n , n , . . . , n 1 2 p 1 2 p Ä 4 in A A, then there is a strand A : i g ‫ގ‬ such that if M is simply bounded in n n . . . n 1 2 i 1 2 i barrelledness condition previous results of the author jointly with J. C. Ferrando are improved here. These results are related to the classical result of Diestel and Faires in vector measures.