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Conditional expectation for operator-valued measures and functions

Published online by Cambridge University Press:  17 April 2009

Brian Jefferies
Affiliation:
Centre for Mathematical Analysis, Australian National University, GPO Box 4, Canberra, ACT 2601, Australia.
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Abstract

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A Radon–Nikodým theorem for operator-valued measures is applied to deduce the existence and uniqueness of conditional expectations in certain cases.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Diestel, J. and Uhl, J.J., Vector measures (Mathematical Surveys, 15. American Mathematical Society, Providence, Rhode Island, 1977).Google Scholar
[2]Hackenbroch, W., “On the Radon–Nikodým theorem for operator measures and its applications to prediction and linear systems theory, 193206 (Lecture Notes in Mathematics, 695. Springer-Verlag, Berlin, Heidelberg, New York, 1978).CrossRefGoogle Scholar
[3]Heinich, H., “Esperance conditionelle pour les fonctions vectorielles”, C.R. Acad. Sci. Paris Sér. A 276 (1973), 935938.Google Scholar
[4]Jefferies, Brian, “The variation of vector measures and cylindrical concentration”, Illinois J. Math. (to appear).Google Scholar
[5]Kluvánek, I., “Operator-valued measures and perturbations of semigroups”, Arch. Rat. Mech. Anal. 81 (1983), 161180.Google Scholar
[6]Kupka, J., “Radon–Nikodým theorems for vector valued measures”, Trans. Amer. Math. Soc. 169 (1972), 197217.Google Scholar
[7]Okada, S., “Integration of vector-valued functions”, Proc. Measure Theory Conf. (Lecture Notes in Mathematics, 1033. Springer-Verlag, Berlin, Heidelberg, New York, 1982).Google Scholar
[8]Schaefer, H.H., Topological vector spaces (Springer-Verlag, New York, Heidelberg, Berlin, 1971).CrossRefGoogle Scholar
[9]Thomas, G.E.F., The Lebesgue–Nikodým theorem for vector-valued Radon measures (Memoirs of the American Mathematical Society, 139. American Mathematical Society, Providence, Rhode Island, 1974).Google Scholar