 Properties of systems can be associated with different parts of the phase space. In the ball example, for instance, the property having positive momentum is associated with the right half of the phase space; that is, it is associated with the set \(\{x \in X \mid p \gt 0\}\). Generalising this idea we say that to every subset \(A\) of a system’s phase space there corresponds a property \(P_A\) so that the system possesses that property at time \(t\) iff the system’s state \(x\) is in \(A\) at \(t\). The subset \(A\) may be arbitrary and the property corresponding to \(A\) may not be intuitive, unlike, for example, the property of having positive momentum. But nothing in the analysis to follow hangs on a property being ‘intuitive’. We then define the event \(A^t\) as the obtaining of \(P_A\) at time \(t\).