Given a monoperiodic setting, my professor defines that if there is no arbitrage opportunity, it means that there is no dominant strategy. This is clear. However he defines that if there is NO dominant strategy, there is a LPM (Linear Pricing Measure). Then, he adds that if the weights are positive then there is no arbitrage opportunity. I did not understand the LPM and what does it mean to have negative weights for a state of the world?