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.
"Quasi-sure analysis, aggregation and dual representations of sublinear expectations in general spaces." Electron. J. Probab. 17 1 - 15, 2012. https://doi.org/10.1214/EJP.v17-2224