A Sufficient and Necessary Condition for G-expectation to be Linear

In general, Peng's g-expectation is a nonlinear mathematical expectation. However, if the function g (t, x, y) satisfies some properties, the g-expectationis expected to be linear. For g-expectation, we have the following conclusions: The necessary and sufficient condition for g-expectation to have linear properties is that the function g has nothing to do with variable y, and g is linear with variable z. In this case, there exists a probability measure Q, under which the linear expectation is equivalent to Peng's g-expectation.