Geodesic
Construction of the Daniell integral with weakened requirements on the class of basic functions
Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 573-580

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The well-known constructions of the Daniell integral suggest that the class of basic functions is closed with respect to lattice-point operations or, what amounts to the same thing, with respect to passage to the modulus function. It is shown that the theory of the Daniell integral can be constructed without this initial assumption. 
@article{MZM_1978_23_4_a8,
     author = {V. P. Panteleev},
     title = {Construction of the {Daniell} integral with weakened requirements on the class of basic functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {573--580},
     publisher = {mathdoc},
     volume = {23},
     number = {4},
     year = {1978},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a8/}
}
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V. P. Panteleev. Construction of the Daniell integral with weakened requirements on the class of basic functions. Matematičeskie zametki, Tome 23 (1978) no. 4, pp. 573-580. http://geodesic.mathdoc.fr/item/MZM_1978_23_4_a8/