Geodesic
Positive Sets and Monotone Sets
Journal of convex analysis, Tome 14 (2007) no. 2, pp. 297-317

Voir la notice de l'article provenant de la source Heldermann Verlag

We show how convex analysis can be applied to the theory of sets that are "positive" with respect to a continuous quadratic form on a Banach space. Monotone sets can be considered as a special case of positive sets, and we show how our results lead to very efficient proofs of a number of results on monotone sets. One of the key techniques that we use is a generalization of the Fitzpatrick function from monotone set theory to an analogous function for positive sets. 
@article{JCA_2007_14_2_JCA_2007_14_2_a5,
     author = {S. Simons},
     title = {Positive {Sets} and {Monotone} {Sets}},
     journal = {Journal of convex analysis},
     pages = {297--317},
     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2007},
     url = {http://geodesic.mathdoc.fr/item/JCA_2007_14_2_JCA_2007_14_2_a5/}
}
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S. Simons. Positive Sets and Monotone Sets. Journal of convex analysis, Tome 14 (2007) no. 2, pp. 297-317. http://geodesic.mathdoc.fr/item/JCA_2007_14_2_JCA_2007_14_2_a5/