Results 1 to 3 of 3

Math Help - ssplitted function integrability prove

  1. #1
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    ssplitted function integrability prove

    3)b)
    there is f(x) a continues and positive in [0,1]

    g(x)=f(x) for rational x
    g(x)=-f(x) for irational x

    prove that g(x) is not integrabile in [0,1]
    ?

    how i tried to solve it:
    suppose that this not true and it integrabile
    so so every dividing p
    inf{S(p)-s(p)}=0
    S(p)=\sum_{i=1}^{n}M_{i}(x_{i}-x_{i-1)}
    s(p)=\sum_{i=1}^{n}m_{i}(x_{i}-x_{i-1)}
    or i need to prove that infE=supT
    now i need to get expresstion and prove that the equations above cannot exist.

    what to do here in general
    ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45

    Re: ssplitted function integrability prove

    One simple way: the set of discontinuity points of f is [0,1] . Taking into account that [0,1] has not measure zero, f is no Riemann integrable (as a consequence of a well known theorem).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    Re: ssplitted function integrability prove

    ok i understand the theory that because of endless points of discontinuety its not differentiable.

    how in general could i show this using the above formulas i wrote
    ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove integrability
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: May 10th 2010, 07:42 PM
  2. Integrability of a function
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2009, 04:11 PM
  3. Integrability of a function
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 18th 2009, 06:44 PM
  4. Integrability of a function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 18th 2009, 06:38 PM
  5. Integrability of a piecewise function
    Posted in the Calculus Forum
    Replies: 0
    Last Post: December 7th 2008, 04:13 PM

Search Tags


/mathhelpforum @mathhelpforum