envelope of a function

Consider f: a real function of real variable.

We call the upper envelope of f to the functionMathworldPlanetmath:


similarly the lower envelope of f is the function:


The envelopes have the following properties: (in this list env represents either the upper or lower envelope)

  • envinf(f)(x)f(x)envsup(f)(x)

  • envsup(f)=envinf(f)fis continuous

  • envsup(f)(x)-envinf(f)(x)=oscillation offat x

  • envinff=-envsup(-f)

Title envelope of a function
Canonical name EnvelopeOfAFunction
Date of creation 2013-03-22 15:44:22
Last modified on 2013-03-22 15:44:22
Owner cvalente (11260)
Last modified by cvalente (11260)
Numerical id 5
Author cvalente (11260)
Entry type Definition
Classification msc 26A99