Geodesic
On the limits of generalization of the Kolmogorov integral
Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 258-272

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The generalization of the Kolmogorov integral to functions with values in a Banach space is considered. It is proved that the resulting integral turns out to be essentially more general than the Bochner integral and is exactly equivalent to an integral of McShane type, whose definition requires that the scaling function be measurable. 
@article{MZM_2005_77_2_a7,
     author = {A. P. Solodov},
     title = {On the limits of generalization of the {Kolmogorov} integral},
     journal = {Matemati\v{c}eskie zametki},
     pages = {258--272},
     publisher = {mathdoc},
     volume = {77},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a7/}
}
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A. P. Solodov. On the limits of generalization of the Kolmogorov integral. Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 258-272. http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a7/