##  [Modulus of Noncompactness](/index.php/modulus-noncompactness) 

  ##  [Modulus of Noncompactness](https://puremath.quantumdictionary.io/modulus-noncompactness-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A numerical quantity assigned to a bounded subset of a metric or Banach space that measures how far the set is from being relatively compact; commonly the Kuratowski measure of noncompactness is the infimum of radii r such that the set can be covered by finitely many balls of radius r.