Abstract
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.
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Translated from Matematicheskie Zametki, vol. 77, no. 2, 2005, pp. 258–272.
Original Russian Text Copyright © 2005 by A. P. Solodov.
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Solodov, A.P. On the limits of generalization of the Kolmogorov integral. Math Notes 77, 232–245 (2005). https://doi.org/10.1007/s11006-005-0023-1
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DOI: https://doi.org/10.1007/s11006-005-0023-1