The task is to show that the absolute value of a regulated function is again a regulated function.
A regulated function is a function $f: [a,b] \rightarrow \mathbb{R}$
For every point in the interval $(a,b)$ exists a limit from both sides.
$$ f (x) = \lim_{n \to \infty} t_n(x) $$
where $t_n(x)$ is a step function in the interval $(a,b)$
My current approaches was the following:
$$ |f(x)| = \lim_{n \to \infty} |t_n(x)| $$
but I'm not sure if it is correct.