Some remarks on vector-valued integration

The paper continues the study of the notion of Riemann–Lebesgue integral, which was introduced before by two of the authors. The result about the convexity of the limit set of integral sums is generalized to the case of weakly-compactly generated spaces. The notion of Riemann–Lebesgue integral is used to introduce new classes of Banach spaces. The properties of these new spaces are studied.