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Additive Functionals on Lorentz Spaces
Published online by Cambridge University Press: 20 November 2018
Abstract
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.
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- Copyright © Canadian Mathematical Society 1984