An ergodic transformation of a probability space 
is a measure-preserving map 
for which every measurable
set 
invariant modulo a set of measure
zero has measure 0 or 1. Equivalently, 
implies 
, where 
denotes the symmetric
difference. A mixing transformation
is ergodic.
Ergodic Transformation
See also
Ergodic Measure, Ergodic Theory, Invariant Measure, Mixing TransformationExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Ergodic Transformation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ErgodicTransformation.html