Geodesic
Additive Functionals on Lorentz Spaces
Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 31-37

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DOI

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.
DOI : 10.4153/CMB-1984-004-3
Mots-clés : 46E30, 47H99 
Ghatage, Pratibha G. Additive Functionals on Lorentz Spaces. Canadian mathematical bulletin, Tome 27 (1984) no. 1, pp. 31-37. doi: 10.4153/CMB-1984-004-3
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     title = {Additive {Functionals} on {Lorentz} {Spaces}},
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     year = {1984},
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     doi = {10.4153/CMB-1984-004-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-004-3/}
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