 ##  [Oscillation](/oscillation) 

  ##  [Oscillation](https://puremath.quantumdictionary.io/oscillation-0) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

The supremal difference between values of a function over arbitrarily small neighborhoods (local oscillation) or the supremum minus infimum over a set (global oscillation), used to quantify local variability: ω_f(x0) = lim_{r→0} sup_{B(x0,r)} f - inf_{B(x0,r)} f. Oscillation measures failure of continuity and refines modulus of continuity.