##  [Ergodic Theorem](/ergodic-theorem) 

  ##  [Ergodic Theorem](https://information.quantumdictionary.io/ergodic-theorem-0) 

  

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**Information & Communication Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For a measure‑preserving dynamical system or a stationary stochastic process that is ergodic, the time average of an integrable observable along almost every single trajectory converges to the ensemble (expected) average; thus long‑time sample means equal probabilistic expectations under the ergodicity conditions.