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.
thanks for the hint.
Because of n=1, we can write .
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?