Lipschitz function

Let WX and f:X. Then f is on W if there exists an M such that, for all x,yW, xy


If a,b with a<b and f:[a,b] is LipschitzPlanetmathPlanetmath on (a,b), then f is absolutely continuousMathworldPlanetmath on [a,b].

Example: Is


We need to estimate the constant M.


It follows that


and f(x) is not Lipschitz at x=0.

Title Lipschitz function
Canonical name LipschitzFunction
Date of creation 2013-03-22 14:01:42
Last modified on 2013-03-22 14:01:42
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 12
Author bwebste (988)
Entry type Definition
Classification msc 26A16
Defines Lipschitz