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Rybakov's theorem in Fréchet spaces and completeness of L1-spaces

Part of: Set functions, measures and integrals with values in abstract spaces

Published online by Cambridge University Press:  09 April 2009

W. J. Ricker
W. J. Ricker
Affiliation:
School of Mathematics University of New South WalesSydney, NSW 2052Australia
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Abstract

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We provide a simple and direct proof of the completeness of the L1-space of any vector measure taking its values in the class of Fréchet spaces which do not contain a copy of the sequence space ω.

MSC classification

Secondary: 28B05: Vector-valued set functions, measures and integrals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 2 , April 1998 , pp. 247 - 252
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Bartle, R. G., Dunford, N. and Schwartz, J. T., ‘Weak compactness and vector measures’, Canad. J. Math. 7 (1955), 289–305.CrossRefGoogle Scholar
[2]Curbera, G. P., ‘Operators into L 1 of a vector measure and applications to Banach lattices’, Math. Ann. 292 (1992), 317–330.CrossRefGoogle Scholar
[3]Curbera, G. P., ‘When L 1 of a vector measure is an AL-space’, Pacific J. Math. 162 (1994), 287–303.CrossRefGoogle Scholar
[4]Fernández, A. and Naranjo, F., ‘Rybakov's theorem for vector measures in Fréchet spaces’, Indag. Math. (New Series) 8 (1997), 33–42.CrossRefGoogle Scholar
[5]Jarchow, H., Locally convex spaces (Teubner, Stuttgart, 1981).CrossRefGoogle Scholar
[6]Kluvánek, I. and Knowles, G., Vector measures and control systems (North Holland, Amsterdam, 1975).Google Scholar
[7]Lewis, D. R., ‘Integration with respect to vector measures’, Pacific J. Math. 33 (1970), 157–165.CrossRefGoogle Scholar
[8]Okada, S., ‘The dual space of L 1 (μ) for a vector measure μ’, J. Math. Anal. Appl. 177 (1993), 583–599.CrossRefGoogle Scholar
[9]Rybakov, V. I., ‘Theorem of Bartle, Dunford and Schwartz on vector-valued measures’, Mat. Zametki 7 (1970), 247–254. English translation:Google Scholar
Math. Notes 7, 147–151.CrossRefGoogle Scholar