Before revision:  By contrast, completeness is a sufficient and necessary condition for a market to be informationally efficient , i.e., only in that case past and future events turn out to be independent conditional on the price history with respect to the physical measure.
After revision:  By contrast, completeness is a sufficient and necessary for a market to be informationally efficient , i.e., only in that case past and future events turn out to be independent conditional on the price history with respect to the physical measure.