##  [Lebesgue Number Lemma](/lebesgue-number-lemma) 

  ##  [Lebesgue Number Lemma](https://puremath.quantumdictionary.io/lebesgue-number-lemma-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A lemma stating that for every open cover of a compact metric space there exists a positive real number (a Lebesgue number) such that every subset of the space with diameter less than that number is contained in some member of the cover.