Multilinear integration of bounded scalar valued functions (Q2702806)

The paper presents a continuation (unfortunately, the last one because of author's death) of a long series of papers devoted to the integration in Banach spaces. It works with \(d\) measurable spaces \((T_i, S_i)\) and a multimeasure \(\gamma \) which is a mapping \(\gamma : S_1 \times S_2 \times\dots\times \rightarrow Y\), where \(Y\) is a Banach space and \(\gamma_i\) is a \(\sigma \)-additive vector measure in each coordinate \(i\). A general convergence theorem extending the multilinear Lebesgue convergence theorem is proved. In this theorem not only convergent sequences of functions are considered, but also convergent sequences of multimeasures. As an application a version of the Fubini theorem is proved.