Integration of Banach-Valued Functions and Haar Series with Banach-Valued Coefficients / V. A. Skvortsov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2017. № 1. P. 25-32 [Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 24-30].
It is proved that for any Banach space each everywhere convergent Haar series with coefficients from this space is the Fourier–Haar series in the sense of Henstock type integral with respect to a dyadic differential basis. At the same time, the almost everywhere convergence of a Fourier–Henstock–Haar series of a Banach-space-valued function essentially depends on properties of the space.
Key words: Haar series, Walsh series, dyadic derivation basis, Henstock integral, Pettis integral, Banach-space-valued functions, Orlicz property.