##  [Ergodic Theory](/ergodic-theory) 

  ##  [Ergodic Theory](https://puremath.quantumdictionary.io/ergodic-theory-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The mathematical study of the long-term statistical behavior of measure-preserving transformations and flows: invariant measures, ergodicity, mixing, recurrence, and the relation between time averages along orbits and spatial averages with respect to an invariant measure.