Hello,

can you please help me to calculate the total variation of the signum function on .

The total variation of , whereas is defined by

.

I don't know how to apply this abstract defintion.

Bye,

Alexander

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- Dec 13th 2011, 12:32 AMAlexanderWTotal variation
Hello,

can you please help me to calculate the total variation of the signum function on .

The total variation of , whereas is defined by

.

I don't know how to apply this abstract defintion.

Bye,

Alexander - Dec 13th 2011, 01:12 AMgirdavRe: Total variation
Here the dimension of is 1, so has a simple expression. So you can compute in terms of .

- Dec 13th 2011, 09:14 AMAlexanderWRe: Total variation
Hello,

thanks for the hint.

Because of n=1, we can write .

It is

I used the Fundamental Theorem of Calculus and ,

because is compact ( ).

Now, by definition it is

with is a zero set.

Because of , choose and then .

Is everything correct?

Bye,

Alexander - Dec 13th 2011, 09:22 AMgirdavRe: Total variation
It seems correct.