Belated integrals
Recent theories of non-commutative stochastic integral have indicated that it is a kind of vector Riemann-Stieltjes integral. Earlier \textit{R. G. Bartle} [Studia Math. 15, 337-352 (1956; Zbl 0070.281)] developed a bilinear vector integral which at first sight appears to be a natural setting for the non-commutative stochastic integral. However it was shown that the non-commutative stochastic integral could not be obtained using Bartle's vector integral. In this paper the authors show that by weakening a few of the requirements of Bartle's theory (on \(R^+)\) they get an integration theory on \(R^+\) which has as special cases each of the integrals described in previous papers of the authors and \textit{R. F. Streater} [see e.g. Math. Proc. Camb. Philos. Soc. 94, 541-551 (1983; Zbl 0546.60037)].
scientific article; zbMATH DE number 4011575
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