Geodesic
Legendre-Type Integrands and Convex Integral Functions
Journal of convex analysis, Tome 21 (2014) no. 1, pp. 261-288.

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

We study the properties of integral functionals induced on L1E (S,μ) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and give various limiting counterexample.
Classification : 46B20, 34H05, 47H05, 47N10, 90C25
Mots-clés : Legendre function, monotone operator, set-valued operator, strongly rotund function, Kadec-Klee property, subdifferential operator, Visintin theorem, Vitali's covering theorem, weak convergence, weak compactness, convergence in measure 
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     author = {J. M. Borwein and L. Yao},
     title = {Legendre-Type {Integrands} and {Convex} {Integral} {Functions}},
     journal = {Journal of convex analysis},
     pages = {261--288},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2014},
     url = {http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a14/}
}
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J. M. Borwein; L. Yao. Legendre-Type Integrands and Convex Integral Functions. Journal of convex analysis, Tome 21 (2014) no. 1, pp. 261-288. http://geodesic.mathdoc.fr/item/JCA_2014_21_1_JCA_2014_21_1_a14/