Some peculiarities of the Henstock and Kurzweil integrals of Banach space-valued functions
In the paper relationships among the spaces of Banach space-valued functions which are Riemann integrable, Riemann-McShane integrable, Bochner integrable, McShane integrable, variationally Henstock integrable or Henstock integrable are investigated. The author presents several nice examples showing that in general the equalities are false. Moreover, a proof (due to C. S. Hoenig) of the equivalence of the Bochner integral and the variational McShane integral is given. This result has been independently proven (by a different method and later) by \textit{C. Wu} and \textit{X. Yao} [J. Math. Stud. 27, No.~1, 32--36 (1994; Zbl 0947.28010)] and -- in a more general setting -- by \textit{L. Di Piazza} and \textit{K. Musiał} [Ill. J. Math. 45, No.~1, 279--289 (2001; Zbl 0999.28006)].
scientific article; zbMATH DE number 2141362