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Math Help - Bounded variation

  1. #1
    MHF Contributor Amer's Avatar
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    Bounded variation

    what we mean when we say this function is of bounded variation please help me

    Thanks
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  2. #2
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    Quote Originally Posted by Amer View Post
    what we mean when we say this function is of bounded variation please help me

    Thanks
    Given f:[a,b] \to \mathbb{R} and a partition P=\{a=t_0 < t_1 < ... < t_n=b \} then the vatiatin of fo over P is V(f,P)=\sum_{n=0}^{n}|f(t_i)-f(t_{i-1}|

    Notice that this is very similar to a Riemann sum.

    Now if we take the supreemum of all partitions of [a,b] This is called the total variation if \sup_{P}=V(f,p) < \infty
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  3. #3
    MHF Contributor Amer's Avatar
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    it is clear now thanks
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