The Class of Functionals which can be Represented by a Supremum
E. Acerbi, Giuseppe Buttazzo, Francesca Prinari · Journal of convex analysis · 2002
We give a characterization of all lower semicontinuous functionals on L^\infty_\mu L μ ∞ which can be represented in the form \mu μ -sup \{ f(x, u): x \in A \} { f ( x , u ) : x ∈ A } . We also show by a counterexample that the representation above may fail if the lower semicontinuity condition is dropped.