Legendre-type integrands and convex integral functions
نویسندگان
چکیده
In this paper, we study the properties of integral functionals induced on LE(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. 2010 Mathematics Subject Classification: Primary 46B20, 34H05; Secondary 47H05, 47N10, 90C25
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