Itinerary of an interval map
= Itinerary of an interval map
Given a finite measurable partition of an interval, the itinerary of $x$ records which partition element contains each iterate $T^n(x)$. Prescribing a finite initial word defines an itinerary cylinder. For the full <tent map>, every length-$N$ binary cylinder has Lebesgue measure $2^{-N}$ up to endpoint conventions, so its itinerary process is a fair i.i.d. <Bernoulli distribution>[Bernoulli process].