Integrability and the Integral of Partial Functions from R into R1

Noboru Endou, Yasunari Shidama, Masahiko Yamazaki

doi:10.2478/v10037-006-0023-y

Integrability and the Integral of Partial Functions from R into R1

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<jats:title>Integrability and the Integral of Partial Functions from R into R<jats:sup>1</jats:sup></jats:title> <jats:p>In this paper, we showed the linearity of the indefinite integral <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="forma.2006.14.issue-4_figure1.gif" xlink:type="simple" /> the form of which was introduced in [11]. In addition, we proved some theorems about the integral calculus on the subinterval of [<jats:italic>a,b</jats:italic>]. As a result, we described the fundamental theorem of calculus, that we developed in [11], by a more general expression.</jats:p>