- Title
- Legendre-type integrands and convex integral functions
- Creator
- Borwein, Jonathan M.; Yao, Liangjin
- Relation
- Journal of Convex Analysis Vol. 21, Issue 1, p. 261-288
- Relation
- http://www.heldermann.de/JCA/JCA21/JCA211/jca21015.htm
- Publisher
- Heldermann Verlag
- Resource Type
- journal article
- Date
- 2014
- Description
- 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.
- Subject
- Legendre function; monotone operator; convergence in measure; set-valued operator; strongly rotund function; Kadec-Klee property; subdifferential operator; Visintin theorem; Vitali's covering theorem; weak convergence; weak compactness
- Identifier
- http://hdl.handle.net/1959.13/1304796
- Identifier
- uon:20926
- Identifier
- ISSN:0944-6532
- Language
- eng
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