Some peculiarities of the Henstock and Kurzweil integrals of Banach space-valued functions.

Abstract

Some examples, due to G. Birkhoff, are used to explore the differences and peculiarities of the Henstock and Kurzweil integrals in abstract spaces. We also include a proof, due to C. S. Hönig, of the fact that the Bochner-Lebesgue integral is equivalent to the variational Henstock-McShane integral.