
Accession Number : AD0701610
Title : A RIEMANNTYPE INTEGRAL THAT INCLUDES LEBESGUESTIELTJES, BOCHNER AND STOCHASTIC INTEGRALS,
Corporate Author : VIRGINIA UNIV CHARLOTTESVILLE
Personal Author(s) : McShane,E. J.
Report Date : 1969
Pagination or Media Count : 57
Abstract : In this memoir we study the integrals defined as the limits of Riemann sums Summation(U(x sub i, A sub i)) in which the class of permitted pairs (x,A) and the nature of the limit process are subjected only to weak hypotheses. For the definition and the earlier theorems the assumptions are quite weak. To prove the deeper theorems, such as the monotone and dominated convergence theorems, we assume stronger hypotheses. However, they remain weak enough to allow us to obtain the LebesgueStieltjes integral and the Bochner integral over locally compact domains, and also a generalization of K. Ito's stochastic integral, as well as several other integrals that have appeared in the literature. (Author)
Descriptors : (*INTEGRALS, STOCHASTIC PROCESSES), INTEGRAL EQUATIONS, GROUPS(MATHEMATICS), BANACH SPACE, MEASURE THEORY, TOPOLOGY, THEOREMS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE