 Before briefly introducing the next element of the analysis let us mention that there is a question about whether the association of probabilities with the measure of the system is reasonable. Prima facie, a measure on a phase space can have a purely geometrical interpretation and need not necessarily have anything to do with the quantification of uncertainty. For instance, we can use a measure to determine the length of a table, but this measure need not have anything to do with uncertainty. Whether or not such an association is legitimate depends on the cases at hand and the interpretation of the measure. However, for systems of interest in statistical physics it is natural and indeed standard to assume that the probability of the system’s state to be in a particular subset of the phase space \(X\) is proportional to the measure of \(A\).