Results 1 to 3 of 3

Math Help - Riemann Integrable Function

  1. #1
    Member
    Joined
    Feb 2009
    From
    Chennai
    Posts
    148

    Riemann Integrable Function

    Let H(x)=k for x =\frac{1}{k} \ (k \in \mathbb{N}) and H(x)=0 elsewhere on [0,1]. Is H riemann integrable?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,697
    Thanks
    1469
    Mistaken post. Sorry.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,658
    Thanks
    1615
    Awards
    1
    Quote Originally Posted by Chandru1 View Post
    Let H(x)=k for x =\frac{1}{k} \ (k \in \mathbb{N}) and H(x)=0 elsewhere on [0,1]. Is H riemann integrable
    Suppose that T = \left\{ {\frac{1}{k}:k \in \mathbb{Z}^ +  } \right\}. That is the set of discontinuities.
    T is countable so the function is Riemann integrable.

    Here is an outline of a proof. In any partition of [0,1] the subinterval that contains 0 contains almost all points of T. The points outside of that can be covered by intervals the sum of their is as small as needed. Thus showing the integral is zero.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Riemann integrable function?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 25th 2011, 01:59 AM
  2. Replies: 3
    Last Post: November 30th 2009, 08:48 AM
  3. proving function is riemann integrable
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 9th 2009, 01:39 AM
  4. Riemann Integrable Function
    Posted in the Differential Geometry Forum
    Replies: 13
    Last Post: May 10th 2009, 05:47 PM
  5. Riemann integrable, function
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 23rd 2009, 08:09 AM

Search Tags


/mathhelpforum @mathhelpforum