Results 1 to 2 of 2

Math Help - example of absolutely continuity

  1. #1
    Newbie
    Joined
    Dec 2010
    Posts
    1

    Wink example of absolutely continuity

    I'm studying Real analysis,

    It's known Lipschitz continuity implies absolutely continuity.

    and Cantor function is an example for uniformly continuous function but not a absolutely continuous function,

    i wonder if in between case, if f(x) is a holder continuous which is uniformly continuous but not lipschistz continuous, what's the result?

    In any reference, the example of absolutely continuous function was Lipshitz but is it true for holder continuous function?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2010
    Posts
    470
    Something that is holder but not lipschistz:

    f(x) = sqrt(x) around x = 0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Series Absolutely Convergent, xn/(1+xn^2) absolutely convergent
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 6th 2011, 01:36 PM
  2. Absolutely clueless...
    Posted in the Algebra Forum
    Replies: 13
    Last Post: January 20th 2011, 07:12 AM
  3. Converge absolutely
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 25th 2010, 04:50 AM
  4. why is this absolutely convergent?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 29th 2009, 08:54 PM
  5. Absolutely no idea how to do this
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: May 6th 2005, 05:22 PM

Search Tags


/mathhelpforum @mathhelpforum