Geodesic
Abstract integral spaces and minimal extensions
Glasgow mathematical journal, Tome 12 (1971) no. 2, pp. 166-178

Voir la notice de l'article provenant de la source Cambridge University Press

The development of the theory of absolute integrals derives from certain key facts. Among them are:(I) An integral is a positive linear functional on a vector lattice, which is continuous in a certain sense.(II) A function equal almost everywhere to a summable function is itself summable.(III) Every measurable function is the pointwise limit of a sequence of elementary step functions.A device that often plays an important role in measure theory, but which has not beenfully exploited in the theory of abstract integrals is that of(IV) the smallest class containing a given class and having a certain property(such as being a σ-ring of sets). It is our purpose in this paper to examine the theory of abstract real-valued absolute integrals axiomatically, in such a way as to isolate and clarify the roles of (I) through (IV). 
Maron, M. J. Abstract integral spaces and minimal extensions. Glasgow mathematical journal, Tome 12 (1971) no. 2, pp. 166-178. doi: 10.1017/S0017089500001270
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