In the book Weak convergence and Empirical Processes, by Aad W. van der Vaart and Jon A. Wellner, on page 81, the notation $l^\infty(\mathcal{F})$ appears, where $\mathcal{F}$ is a set of measurable functions, $f \in \mathcal{F}$ then $f \colon \mathcal{X} \rightarrow \mathbb{R}$.
I am not sure what $l^\infty(\mathcal{F})$ is. I know what $l^\infty$ is by itself, the set of bounded sequences (Wikipedia), but not sure about this one.