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I want to know the definition of non-periodic bounded variation function. I know the definition for periodic function of bounded variation, which is,

Let $f:[a,b]\to \mathcal c$ and $P=\{a=x_{0},x_{1},....,x_{n}=b\}$ be any partition of $[a,b]$. Set $$V_{P}(f)=\sum_{k=0}^{n-1}|f(x_{k+1})-f(x_{k})|.$$ If $\displaystyle V(f)=\sup_{P}V_{P}(f)<+\infty$ then we say that $f$ is of bounded variation the number $V(f)$ is called the total variation of $f$.

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The definition is the same. See en.wikipedia.org/wiki/Bounded_variation –  Jonas Meyer Jun 5 '12 at 8:35
    
Can you please explain the definition of non-periodic BV function by an example? –  Kns Jun 5 '12 at 8:41
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Do you know an example of a periodic BV function? There is no difference in how BV works for periodic and nonperiodic functions. –  Jonas Meyer Jun 5 '12 at 8:50

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