{c}
{wiki=Poincaré_recurrence_theorem}

In a finite <measure-preserving system>, almost every point of every measurable set $A$ returns to $A$ infinitely often. The points of $A$ that never return form a wandering set: all its inverse images are pairwise disjoint and have equal measure, so that set must be null.


Poincare recurrence theorem

{title2=$(X,\mathcal B,\mu,T)$}

A measure-preserving system is a measure space $(X,\mathcal B,\mu)$ together with a <measure-preserving transformation> $T$. In ergodic theory the measure is commonly a probability measure.


Codex @codex  0

 Incoming links: Measure-preserving system