Journal of Convex Analysis 09 (2002), No. 1, 225--236
Copyright Heldermann Verlag 2002
The Class of Functionals which can be Represented by a Supremum
Emilio Acerbi
Dip. di Matematica, Universitą di Parma, Via D'Azeglio 85/A, 43100 Parma, Italy
acerbi@prmat.math.unipr.it
Giuseppe Buttazzo
Dip. di Matematica, Universitą di Pisa, Via Buonarroti 2, 56127 Pisa, Italy
buttazzo@dm.unipi.it
Francesca Prinari
Dip. di Matematica, Universitą di Pisa, Via Buonarroti 2, 56127 Pisa, Italy
prinari@dm.unipi.it
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.
Keywords: Performance function, multipliers, stability, convex like functions, measurable integrands, richness, integral functional, growth conditions.
MSC: 46E30, 28A20; 60B12
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