Integrals for functions with values in a partially ordered vector space - van Rooij, A. C. M.; van Zuijlen, W. B. (Positivity : an international journal devoted to the theory and applications of positivity in analysis, 2016)
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.