On weak integrability and boundedness in Banach spaces |
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| Authors: | Trond A. Abrahamsen,Olav Nygaard,Mä rt Põ ldvere |
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| Affiliation: | a Department of Mathematics, Agder University College, Servicebox 422, 4604 Kristiansand, Norway
b Institute of Pure Mathematics, University of Tartu, J. Liivi 2, 50409 Tartu, Estonia |
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| Abstract: | Thin and thick sets in normed spaces were defined and studied by M.I. Kadets and V.P. Fonf in 1983. In this paper, we give a new characterization of thick sets in terms of weak integrability of Banach space valued measurable functions. We also characterize thick sets in terms of boundedness of vector measures, and explain how this concept is related to the theory of barrelled spaces. |
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| Keywords: | Thick set Weak integrability Boundedness of vector measures |
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