Integrals for functions with values in a partially ordered vector space

We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure space leads to the classical space of integrable functions.

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Bibliographische Detailangaben
Veröffentlicht in:	Positivity : an international journal devoted to the theory and applications of positivity in analysis Jg. 20; H. 4; S. 877 - 916
Hauptverfasser:	van Rooij, A. C. M., van Zuijlen, W. B.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Cham Springer International Publishing 01.12.2016 Springer Nature B.V
Schlagworte:	Algebra Calculus of Variations and Optimal Control; Optimization Econometrics Fourier Analysis Integrals Mathematical functions Mathematical models Mathematics Mathematics and Statistics Operator Theory Potential Theory Studies Theorems Vector space Partially ordered vector space Vertical extension Riesz space Lateral extension Bochner integral Integral 28B05 28B15 Pettis integral
ISSN:	1385-1292, 1572-9281
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We consider integration of functions with values in a partially ordered vector space, and two notions of extension of the space of integrable functions. Applying both extensions to the space of real valued simple functions on a measure space leads to the classical space of integrable functions.
Bibliographie:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23
ISSN:	1385-1292 1572-9281
DOI:	10.1007/s11117-015-0392-y