Volterra's Function

In mathematics, Volterra's function, named for Vito Volterra, is a real-valued function V defined on the real line R with the following curious combination of properties:

  • V is differentiable everywhere
  • The derivative V ′ is bounded everywhere
  • The derivative is not Riemann-integrable.

Read more about Volterra's Function:  Definition and Construction, Further Properties

Famous quotes containing the word function:

    “The mother’s and father’s attitudes toward the child correspond to the child’s own needs.... Mother has the function of making him secure in life, father has the function of teaching him, guiding him to cope with those problems with which the particular society the child has been born into confronts him.”
    —Erich Fromm (1900–1980)