Editing Bernoulli process (section)

===Odometer===
{{main article|Markov odometer}}
Another way to create a dynamical system is to define an [[Markov odometer|odometer]]. Informally, this is exactly what it sounds like: just "add one" to the first position, and let the odometer "roll over" by using [[carry bit]]s as the odometer rolls over. This is nothing more than base-two addition on the set of infinite strings.  Since addition forms a [[group (mathematics)]], and the Bernoulli process was already given a topology, above, this provides a simple example of a [[topological group]].

In this case, the transformation <math>T</math> is given by
:<math>T\left(1,\dots,1,0,X_{k+1},X_{k+2},\dots\right) = \left(0,\dots,0,1,X_{k+1},X_{k+2},\dots \right).</math> 

It leaves the Bernoulli measure invariant only for the special case of <math>p=1/2</math> (the "fair coin"); otherwise not. Thus, <math>T</math> is a [[measure preserving dynamical system]] in this case, otherwise, it is merely a [[conservative system]].