Integration on measure chains

被引：57

作者：

Aulbach, B ^{[1
]}

Neidhart, L ^{[1
]}

机构：

[1] Univ Augsburg, Dept Math, D-86135 Augsburg, Germany

来源：

PROCEEDINGS OF THE SIXTH INTERNATIONAL CONFERENCE ON DIFFERENCE EQUATIONS: NEW PROGRESS IN DIFFERENCE EQUATIONS | 2004年

关键词：

measure chain; time scale; Cauchy integral; Riemann integral; Cauchy-Riemann integral; Borel integral; Lebesgue integral; Bochner integral;

D O I：

10.1201/9780203575437.ch20

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In its original form the calculus on measure chains is mainly a differential calculus. The notion of integral being used, the so-called Cauchy integral, is defined by,means of antiderivatives and, therefore, it is too narrow for the development of a full infinitesimal calculus. In this paper, we present several other notions of integral such as the Riemann, the Cauchy-Riemann, the Borel and the Lebesgue integral for functions from a measure chain to an arbitrary real or complex Banach space. As in ordinary calculus, of those notions only the Lebesgue integral provides a concept which ensures the extension of the original calculus on measure chains to a full infinitesimal calculus including powerful convergence results and complete function spaces.

引用

页码：239 / 252

页数：14