Results 1 to 3 of 3

Math Help - integral norm proving

  1. #1
    Junior Member
    Joined
    Oct 2012
    From
    uk
    Posts
    41

    integral norm proving

    show that ||f||1 = ∫|f| (integral from 0 to 1) does define a norm on the subspace C[0,1] of continuous functions
    (there are 3 conditions , i just dont know how to prove that ||v||>0,||v||=0 implies v=0)
    and also the same for ||f||= ∫t|f(t)|dt is a norm on C[0,1]
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,881
    Thanks
    697

    Re: integral norm proving

    Hey cummings123321.

    For the ||v|| > 0 consider the definition of the integral and how you partition it up and add up these partitions. Each partition will be positive which means the norm will be positive and zero only if all elements are zero since the sum of all positive things can only be zero if all are zero.

    You will need to specify what kind of integral you are using (because it won't be the Riemann integral for C[0,1]).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2012
    From
    uk
    Posts
    41

    Re: integral norm proving

    Quote Originally Posted by chiro View Post
    Hey cummings123321.

    For the ||v|| > 0 consider the definition of the integral and how you partition it up and add up these partitions. Each partition will be positive which means the norm will be positive and zero only if all elements are zero since the sum of all positive things can only be zero if all are zero.

    You will need to specify what kind of integral you are using (because it won't be the Riemann integral for C[0,1]).
    yes ,i worked out the first part, but how about the secound ∫t|f(t)| i should get an inequality that smaller than t|f(t)| and greater than 0,but i dont how to get it
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need help proving norm equivalence theorem
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: September 21st 2012, 12:41 PM
  2. Replies: 3
    Last Post: July 13th 2010, 06:37 PM
  3. Replies: 2
    Last Post: November 7th 2009, 12:13 PM
  4. Help with proving norm matrixes
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: October 25th 2009, 12:05 PM
  5. Euclidean Norm and Maximum Norm
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 7th 2009, 04:26 AM

Search Tags


/mathhelpforum @mathhelpforum