On a representation theorem of Schmeidler

In the present paper we consider functionals which occur naturally in the context of generalized certainty equivalents. The common feature of these functionals is that they behave additively for similarly ordered functions. It will be shown that this property allows to associate in a natural way certain martingales to the functions (acts) in question. As a consequence of elementary facts from martingale limit theory we derive an integral representation if the functional has an additional continuity property.