So I was reading this paper and I saw this nonsmooth nonlinear function. But, I am not familiar with this kind of notation, does it denote some kind of a step-function with the value $1$ if $X \leq a$ True and $0$ otherwise?
$$g_0,_j(X_{ji})=4[1(X_{ji}\leq0.25)+1(X_{ji}\leq0.5)+1(X_{ji}\leq0.75)-1.5]$$
What you are looking for is an Indicator function: wiki, which is defined as follows
$$1_A(x) :=\begin{cases} 1, & \text{ if } x\in A,\\ 0, & \text{ otherwise} \end{cases}$$
As an alternative notation, one may also give:
$$1(x\in A) :=\begin{cases} 1, & \text{ if } x\in A,\\ 0, & \text{ otherwise} \end{cases}$$
In your case, the second notation is used. Therefore $1(X_{ji}\leq 0.25) =\begin{cases} 1, & \text{ if } X_{ji}\leq0.25,\\ 0, & \text{ otherwise}\end{cases}$
