##  [Modulus of Smoothness](/modulus-smoothness) 

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

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A modulus of smoothness is a functional that quantifies the smoothness of a function by measuring the size of its finite differences at varying scales. Typically defined via rth‑order differences Δ_h^r f and a scale parameter t, it yields a nonnegative function ω(f,t) that decreases to zero at small t for smoother functions.