oscillation of a function

Definition 1.

Let f:XRR. The oscillation of the functionMathworldPlanetmath f on the set X is said to be


where a,b are arbitrary points in X.

0.1 Examples

  • ω(x2,[-1,2])=4

  • ω(x,[-1,2])=3

  • ω(x,(-1,2))=3

  • ω(sgnx[-1,2])=2

  • ω(sgnx[0,2])=1

  • ω(sgnx(0,2])=0

Cauchy’s criterion can be expressed in terms of this concept.[1]


Title oscillation of a function
Canonical name OscillationOfAFunction
Date of creation 2013-03-22 17:45:50
Last modified on 2013-03-22 17:45:50
Owner perucho (2192)
Last modified by perucho (2192)
Numerical id 5
Author perucho (2192)
Entry type Definition
Classification msc 26A06
Related topic TotalVariation