Convex transformations with Banach lattice range.
Stochastica, Tome 11 (1987) no. 1, p. 13.

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A closed epigraph theorem for Jensen-convex mappings with values in Banach lattices with a strong unit is established. This allows one to reduce the examination of continuity of vector valued transformations to the case of convex real functionals. In particular, it is shown that a weakly continuous Jensen-convex mapping is continuous. A number of corollaries follow; among them, a characterization of continuous vector-valued convex transformations is given that answers a question raised by Ih-Ching Hau.
Classification : 46B42, 46A40, 26A51
Mots-clés : Espacios de Banach, Funciones convexas, Funciones continuas, closed epigraph theorem, strong unit, Jensen-convex, convex analogue of the Banach closed graph theorem, real linear topological Baire space, Banach lattice with strong unit 
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     author = {Roman Ger},
     title = {Convex transformations with {Banach} lattice range.},
     journal = {Stochastica},
     pages = {13},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {1987},
     mrnumber = {MR0970259},
     zbl = {0675.46012},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/STO_1987__11_1_38975/}
}
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Roman Ger. Convex transformations with Banach lattice range.. Stochastica, Tome 11 (1987) no. 1, p. 13. https://geodesic-test.mathdoc.fr/item/STO_1987__11_1_38975/