Before revision:  The superhedging problem is formulated with simple trading strategies  and superhedging is required in the pathwise sense on a \sigma-compact sample space of price trajectories.
After revision:  The superhedging problem is formulated with simple trading strategies , the claim is the limit inferior of continuous functions, which allows for upper and lower semi-continuous claims, and superhedging is required in the pathwise sense on a \sigma-compact sample space of price trajectories.