Abstract

We give a characterization of all lower semicontinuous functionals on Lm¥ which can be represented in the form m-sup{ f(x, u): x from A }. We also show by a counterexample that the representation above may fail if the lower semicontinuity condition is dropped.

Author information

Contact details are reproduced from the original publication and may be historical.

Giuseppe Buttazzo

Dip. di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy

buttazzo@dm.unipi.it

Francesca Prinari

Dip. di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy

prinari@dm.unipi.it

Keywords

  • Performance function
  • multipliers
  • stability
  • convex like functions
  • measurable integrands
  • richness
  • integral functional
  • growth conditions

Mathematics Subject Classification

46E30, 28A20; 60B12

Suggested citation

E. Acerbi, G. Buttazzo, F. Prinari. “The Class of Functionals which can be Represented by a Supremum.” Journal of Convex Analysis 9 (2002), No. 1, 225–236.

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Published by Heldermann Verlag, 2002. Rights now held by Banach Press.