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A note on absolute continuity

โœ Scribed by Lawrence Zalcman


Publisher
Elsevier Science
Year
1968
Tongue
English
Weight
109 KB
Volume
24
Category
Article
ISSN
0022-247X

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We prove that in any dimension a variational measure associated with an additive continuous function is ฯƒ-finite whenever it is absolutely continuous. The one-dimensional version of our result was obtained in [1] by a different technique. As an application, we establish a simple and transparent rela

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We show that a Banach space X has the analytic complete continuity property if and only if for every 1 โ‰ค p < โˆž and for every f โˆˆ H p X , the sequence f r n e iโ€ข is p-Pettis-Cauchy for every r n โ†‘ 1. This allows us to show that X has the analytic complete continuity property if and only if L p X has