Bochner integrals in ordered vector spaces

Bochner integrals in ordered vector spaces

We present a natural way to cover an Archimedean directed ordered vector space E by Banach spaces and extend the notion of Bochner integrability to functions with values in E . The resulting set of integrable functions is an Archimedean directed ordered vector space and the integral is an order pres...

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2017-09, Vol.21 (3), p.1089-1113
Hauptverfasser: van Rooij, A. C. M., van Zuijlen, W. B.
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Integrals
Mathematical functions
Mathematics
Mathematics and Statistics
Operator Theory
Potential Theory
Vector space
Vector spaces
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Zusammenfassung:We present a natural way to cover an Archimedean directed ordered vector space E by Banach spaces and extend the notion of Bochner integrability to functions with values in E . The resulting set of integrable functions is an Archimedean directed ordered vector space and the integral is an order preserving map.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-016-0454-9