摘要

The main goal of this article is to investigate the integration theory of Mcshanetype for functions with values in ordered spaces. Afected by the work ofBoccuto, Riecan, and Vr芍belov芍 with Kurzweil-Henstock integration we studiedthe same problems for another important type of integration on such space asMcshane ones.In this paper we present in other way the definition of Mcshaneintegral on the Riesz space using a very important lemma of famous Fremlin. Inthe second section we reconstruct allmost all the propeties of Mchane integralgiven in [5], [6] and these ones become a little more stronger. We arrive somenew results compared with Henstock-Kurzweil ones. In the third section wedefine the strong version of Mcshane integral and give the neccesary and sufficentcondition of this concept. In the fourth section we prove the fundamentaltheorems of Calculus for the DM-integral and in the fifth we extended anapplication of this integration to Walsh series.

  • 出版日期2013

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