Continuous-time trading and the emergence of randomness

A new definition of events of game-theoretic probability zero in continuous time is proposed and used to prove results suggesting that trading in financial markets results in the emergence of properties usually associated with randomness. This paper concentrates on 'qualitative' results, stated in terms of order (or order topology) rather than in terms of the precise values taken by a price process. No stochastic assumptions are made, and the only assumption is that the price process is continuous.