Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces

Samuel N. Cohen

Published 2011-10-12, updated 2011-10-26Version 2

We consider coherent sublinear expectations on a measurable space, without assuming the existence of a dominating probability measure. By considering a decomposition of the space in terms of the supports of the measures representing our sublinear expectation, we give a simple construction, in a quasi-sure sense, of the (linear) conditional expectations, and hence give a representation for the conditional sublinear expectation. We also show an aggregation property holds, and give an equivalence between consistency and a pasting property of measures.