Notation for a function definition I came across the following notation in a research paper

Suppose we have a function $f(x) \in [1,l] \rightarrow \mathbb{R}$

It is the first time, I am looking such a notation. And the paper is using the same notation for all functions used in it.
Is it same as
$f(x) : [1,l] \rightarrow \mathbb{R}$
If yes, is it an abuse of notation?
If no, what does the notation mean?

In the paper you're using, I understand it means that $f$ belongs to the set of all functions defined from the set $[1,l]$ to the set $\mathbb{R}$, to be said,
$$[1,l]\to\mathbb{R} := \{f \text{ function }: f \text{ is defined from $[1,l]$ to $\mathbb{R}$}\}$$
so it works the same way as defining $f$ the usual way, to be said:
$$f\in[1,l]\to\mathbb{R} \equiv f:[1,l]\to\mathbb{R}$$
