Results 1 to 2 of 2

Thread: Metric of C[0,1]

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Metric of C[0,1]

    Consider the set of $\displaystyle C[0,1]$, the set of all continuous functions on [0,1], and define $\displaystyle p(f,g)= \int ^1 _0 \mid f-g \mid dx $.

    Prove that if $\displaystyle p(f,g)=0$, then f = g.


    If $\displaystyle p(f,g)=0$, then I have $\displaystyle \int ^1 _0 \mid f(x)-g(x) \mid dx =0$.

    But now, what can I do with the absolute values? Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member flyingsquirrel's Avatar
    Joined
    Apr 2008
    Posts
    802
    Quote Originally Posted by tttcomrader View Post
    But now, what can I do with the absolute values?
    Use this property: If $\displaystyle h\in C[0,1]$ is a non-negative function such that $\displaystyle \int_0^1h(x)\,\mathrm{d}x = 0$ then $\displaystyle h=0$.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: Sep 17th 2011, 03:44 PM
  2. [SOLVED] Euclidean metric is a metric
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: Jan 14th 2011, 12:13 AM
  3. Limit of function from one metric space to another metric space
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Sep 17th 2010, 02:04 PM
  4. Metric
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Aug 15th 2010, 02:46 AM
  5. standard metric and discrete metric
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Mar 24th 2009, 07:25 AM

Search Tags


/mathhelpforum @mathhelpforum