Another example of duality between game-theoretic and measure-theoretic probability

This paper makes a small step towards a non-stochastic version of superhedging duality relations in the case of one traded security with a continuous price path. Namely, we prove the coincidence of game-theoretic and measure-theoretic expectation for lower semicontinuous positive functionals. We consider a new broad definition of game-theoretic probability, leaving the older narrower definitions for future work.