 There are, of course, many different ways of partitioning a phase space. In what follows we are going to study how different partitions relate to each other. An important concept in this connection is independence. Let \(\alpha\) and \(\beta\) be two partitions of \(X\). By definition, these partitions are independent iff \(\mu(\alpha_i \cap \beta_j) = \mu(\alpha_i)\mu(\beta_j)\) for all atoms \(\alpha_i\) of \(\alpha\) and all atoms \(\beta_j\) of \(\beta\). We will explain the intuitive meaning of this definition (and justify calling it ‘independence’) in Section 4; for the time being we just use it as a formal definition.