Before revision:  The existence of such a scheme, whose practical value is tempered by its use of the Axiom of Choice , shows that imposing regularity conditions (such as measurability) is essential even in the foundations of game-theoretic probability .
After revision:  The existence of such a scheme, whose practical value is tempered by their use of the Axiom of Choice , shows that imposing regularity conditions (such as measurability) is essential even in the foundations of game-theoretic probability .