##  [Martingale Convergence Theorem](/martingale-convergence-theorem) 

  ##  [Martingale Convergence Theorem](https://natural.quantumdictionary.io/martingale-convergence-theorem-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A result stating that a martingale sequence (with respect to a given filtration) that is uniformly integrable or bounded in L^1 converges almost surely and in L^1 to a limiting random variable measurable with respect to the terminal σ-algebra.