 Furthermore, EH can be used to characterize randomness and chaos in both ergodic and non-ergodic systems. Even if a system as a whole is not ergodic (i.e., if it fails to be ergodic with respect to the entire phase space \(X)\), there can be (and usually there are) subsets of \(X\) on which the system is ergodic. This is what Lichtenberg and Libermann (1992, p. 295) have in mind when they observe that ‘[i]n a sense, ergodicity is universal, and the central question is to define the subspace over which it exists’. In fact, non-ergodic systems may have subsets that are not only ergodic, but even Bernoulli! It then becomes interesting to ask what these subsets are, what their measures are, and what topological features they have. These are questions studied in parts of dynamical systems theory, most notably KAM theory. Hence, KAM theory does not demonstrate that ergodic theory is not useful in analyzing the dynamical behavior of real physical systems (as is often claimed). Indeed, KAM systems have regions in which the system manifest either merely ergodic or Bernoulli behaviour, and accordingly EH is useful for charactering the dynamical properties of such systems (Berkovitz, Frigg and Kronz 2006, Section 4). Further, as we have mentioned in Section 4.1, almost all Hamiltonian systems are non-integrable, and accordingly they have large regions of the phase space in which their motion is ergodic-like. So EH is a useful tool in studying the dynamical properties of systems even if the system fails to be ergodic tout court.