Results 1 to 2 of 2

Math Help - bounded variation function

  1. #1
    Junior Member
    Joined
    Mar 2009
    Posts
    44

    bounded variation function

    f is bounded variation function iff there exist non-decreasing function g such that f(x_2)-f(x_1) < g(x_2)-g(x_1) for x_1 < x_2

    Can anybody help me with this proof? Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,962
    Thanks
    1784
    Awards
    1
    Quote Originally Posted by sidi View Post
    f is bounded variation function iff there exist non-decreasing function g such that f(x_2)-f(x_1) < g(x_2)-g(x_1) for x_1 < x_2
    Can anybody help me with this proof?
    Define g(x) = \sup \left\{ {\sum\limits_{j = 1}^n {\left| {f(x_j ) - f(x_{j - 1} )} \right|} :\left\{ {x_0 ,x_1 , \cdots x_n } \right\}} \text{ is a partition of }[a,x]\right\}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Question about bounded variation
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 14th 2010, 01:51 PM
  2. bounded variation
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: December 24th 2009, 08:38 PM
  3. bounded variation
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: November 3rd 2009, 07:37 PM
  4. bounded variation
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: August 12th 2009, 05:28 PM
  5. Bounded variation
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 29th 2009, 11:53 AM

Search Tags


/mathhelpforum @mathhelpforum