  One important feature of this dynamics is that it is measure preserving, so that if \(X\) is a subset of the unit square, \(\mu(X) = \mu(\phi(X))\). (This is easily seen, as the symbol shift dynamics on the basic sets of infinite binary sequences is measure-preserving, and each coordinate can be represented as an infinite binary sequence.) Define the set \(L = \{(p, q) : 0 \le p \lt \frac{1}{2} \}\). We see that \((p, q) \in L\) iff \(p_1 = 0\). Since \(p\) can be represented by an infinite binary sequence, and a measure one set of finite binary sequences is Borel normal, we see that almost all states of this system are such that, over time, \(\mu(\phi(s) \in L \mid s \in L) = \mu(\phi(s) \in L)\)—that is, whether the system is in \(L\) at \(t\) is probabilistically independent of its past history. Furthermore, \(\mu(L) = \mu(\overline{L})\). The behaviour of this system over time, with respect to the partition  \(\{L, \overline{L}\}\), is therefore a Bernoulli process, exactly like a sequence of fair coin tosses—a series of independent and identically distributed repetitions of a chance process. If the RCT is true, then a system which behaves exactly like a chance process should have as its product a random sequence. So the sequence of outcomes for the baker’s transformation (under this partition) is a random sequence.