Abstract

We study the properties of integral functionals induced on LE1(S,μ)L^1_E(S,\mu) 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.

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Keywords

  • 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

Mathematics Subject Classification

46B20, 34H05; 47H05, 47N10, 90C25

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Suggested citation

J. M. Borwein, L. Yao. “Legendre-Type Integrands and Convex Integral Functions.” Journal of Convex Analysis 21 (2014), No. 1, 261–288. https://doi.org/10.68381/jca21015

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Published by Heldermann Verlag, 2014. Rights now held by Banach Press.