##  [Dominated Convergence](/dominated-convergence) 

  ##  [Dominated Convergence](https://puremath.quantumdictionary.io/dominated-convergence-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The theorem and method that allow passing the limit inside an integral: if a sequence of measurable functions f_n converges pointwise almost everywhere to f and there exists an integrable function g with |f_n| ≤ g almost everywhere for all n, then ∫ f_n → ∫ f and f is integrable.