A necessary and sufficient condition for probability measures dominated by g-expectation

We prove that if the generator g of a g-expectation epsilon(g). is independent of y, then a probability measure Q is dominated by epsilon(g) if and only if Q can be generated by the Girsanov transformation via a controlled process; furthermore, we prove that epsilon(g) equals the supremum of its dominated mathematical expectations if and only if g is sublinear with respect to z. (c) 2008 Elsevier B.V. All rights reserved.