# Thread: Bounded variation

1. ## Bounded variation

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

Thanks

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

3. it is clear now thanks