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The Ward property for a P-adic basis and the P-adic integral

✍ Scribed by B. Bongiorno; L. Di Piazza; V.A. Skvortsov

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 145 KB
Volume: 285
Category: Article
ISSN: 0022-247X
DOI: 10.1016/s0022-247x(03)00426-8

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✦ Synopsis

An Henstock-Kurzweil type integral with respect to a P-adic basis is considered. It is shown that a P-adic basis possesses the Ward property if and only if the sequence by which it is defined is bounded. As a consequence, some full descriptive characterizations of the P-adic integral in the bounded case are obtained. Moreover, an example of an exact P-adic primitive which is not a VBG function and does not satisfy the Lusin condition (N) is constructed.

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