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

被引：9

作者：

Bongiorno, B

Di Piazza, L

Skvortsov, VA

机构：

[1] Dipartimento Matemat, I-90123 Palermo, Italy

[2] Moscow MV Lomonosov State Univ, Dept Math, Moscow 119992, Russia

[3] Akad Bydgoska, Inst Matemat, PL-85072 Bydgoszcz, Poland

[4] Moscow MV Lomonosov State Univ, Dept Math, Moscow 119992, Russia

[5] Dipartimento Matemat, I-90123 Palermo, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2003年 / 285卷 / 02期

关键词：

P-adic basis; P-derivative; ward property; variational measure; Henstock-Kurzweil integral; VBG function;

D O I：

10.1016/S0022-247X(03)00426-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：578 / 592

页数：15

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