Integral of Map into Abelian $\Omega$-group

Aleks Kleyn

Integral of Map into Abelian $\Omega$-group

General Mathematics 2015-03-16 v2

Authors: Aleks Kleyn

Abstract

The common in ring, module and algebra is that they are Abelian group with respect to addition. This property is enough to study integration. I treat integral of measurable map into normed Abelian $\Omega$ -group. Theory of integration of maps into $\Omega$ -group has a lot of common with theory of integration of functions of real variable. However I had to change some statements, since they implicitly assume either compactness of range or total order in $\Omega$ -group.

Keywords

integration theory Abelian groups Omega-groups measurable maps normed groups non-commutative integration

Cite

@article{arxiv.1310.5591,
  title  = {Integral of Map into Abelian $\Omega$-group},
  author = {Aleks Kleyn},
  journal= {arXiv preprint arXiv:1310.5591},
  year   = {2015}
}

Comments

English text - 77 pages; Russian text - 79 pages

Integral of Map into Abelian $\Omega$-group

Abstract

Keywords

Cite

Comments

Related papers