Some remarks on vector-valued integration

Анотація

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.