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On products of vector measures

Published online by Cambridge University Press:  09 April 2009

U. K. Bandyopadhyay
U. K. Bandyopadhyay
Affiliation:
Department of Mathematics, University of Cininnati, Cincinnati, Ohio 45221, U. S. A.
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Products of positive measures play a very important role in analysis. The purpose of this paper is to construct a theory of products of two measures taking values in two (possibly different) Banach spaces. A Fubini theorem is obtained which generalizes the Fubinitheorem for the Bochner integral (Dunford and Schwartz (1958), Theorem 9, page 190), and hence also the classical result.

We use the theory of vector integration presented in Dinculeanu (1967). Our arguments rely upon a standard sort of application of the dominated convergence theorem (cf. Dunford and Schwartz (1958), Theorem 9, page 190), and therefore do not appear to generalize to any theory of integration where this theorem is lacking (e.g. Bartle (1956)).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 1 , February 1975 , pp. 91 - 96
Copyright
Copyright © Australian Mathematical Society 1975

References

Bartle, R. G. (1956), ‘A general bilinear vector integral’, Studia Math. 15, 337–352.CrossRefGoogle Scholar
Bogdanowicz, W. M. (1965), ‘Fubini theorems for generalized Lebesgue-Bochner-Stieltjes integral’, Proc. Japan Acad. 41, 979–983.CrossRefGoogle Scholar
Dinculeanu, N. (1967), Vector measures, (Pergamon, NewYork, 1967.)CrossRefGoogle Scholar
Duchoň, M. (1967), ‘On the projective tensor product of vector valued measures’, Mat. Časopis Sloven. Akad. Vied 17, 113–120.Google Scholar
Duchoň, M. and Kluvánek, I. (1967), ‘Inductive tensor product of vector valued measures’, Mat. Časopis Sloven. Akad. Vied 17, 108–112.Google Scholar
Dunford, N. and Schwartz, J. T. (1958), Linear operators. I: General theory, Pure and Appl. Math. 7, (Interscience, New York, 1958).Google Scholar