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Additive Functionals on Lorentz Spaces

Published online by Cambridge University Press:  20 November 2018

Pratibha G. Ghatage
Pratibha G. Ghatage*
Affiliation:
The Cleveland, State University Department Of Mathematics ClevelandOhio 44115
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Abstract

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If (X, β, μ) is a σ-finite, non-atomic measure space, and ϕ is an increasing non-negative concave function defined on the positive real numbers, we give a set of necessary and sufficient conditions for an additive functional T on the Lorentz space Nϕ to have an integral representation with a Caratheodory kernel. In the special case when T is statistical we classify the functional properties (enjoyed by the kernels) in terms of the Lorentz norm on the space.

Keywords

46E3047H99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 1 , 01 March 1984 , pp. 31 - 37
Copyright
Copyright © Canadian Mathematical Society 1984

References

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