Let f be a measure-preserving transformationPlanetmathPlanetmath of a probability space (X,𝒜,μ). We say that f is mixing (or strong-mixing) if for all A,B𝒜,


and f is weakly mixing if


for all A,B𝒜.

Every mixing transformation is weakly mixing, and every weakly mixing transformation is ergodic.

Title mixing
Canonical name Mixing
Date of creation 2013-03-22 14:06:34
Last modified on 2013-03-22 14:06:34
Owner Koro (127)
Last modified by Koro (127)
Numerical id 6
Author Koro (127)
Entry type Definition
Classification msc 37A25
Defines strongly mixing
Defines strong mixing
Defines strong-mixing
Defines weak-mixing
Defines weakly mixing
Defines weak mixing