 Before we can provide such an analysis, two further steps are needed. First, if the probabilities are to be useful to understanding randomness in a dynamical system, the probability assignment has to reflect the properties of the system. So we have to connect the above probabilities to features of the system. The natural choice is the system’s measure  \(\mu\).[21]  So we postulate that the probability of an event \(A^t\) is equal to the measure of the set \(A: p(A^{t}) = \mu(A)\) for all \(t\). This can be generalised to joint probabilities as follows: