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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Bibliographic Details
Published in:Positivity : an international journal devoted to the theory and applications of positivity in analysis Vol. 20; no. 4; pp. 877 - 916
Main Authors: van Rooij, A. C. M., van Zuijlen, W. B.
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.12.2016
Springer Nature B.V
Subjects:
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 Access:Get full text
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Description
Summary: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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ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-015-0392-y