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This paper makes a small step towards a non-stochastic version ofsuperhedging duality relations in the case of one traded security with acontinuous price path. Namely, we prove the coincidence of game-theoretic andmeasure-theoretic expectation for lower semicontinuous positive functionals. Weconsider a new broad definition of game-theoretic probability, leaving theolder narrower definitions for future work.

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