Bounded variation

**Amer** · May 29th 2009, 06:06 AM

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

Thanks

**TheEmptySet** · May 29th 2009, 07:17 AM

Originally Posted by Amer

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 $\sup_{P}=V(f,p) < \infty$

**Amer** · May 29th 2009, 10:53 AM

it is clear now thanks

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