I don't understand the meaning of the following sentence:
the approximation power of the function set is usually measured w.r.t (with respect to) some fixed reference class $G$ $$\sup_{g \in G} \inf_{f \in F} \| f - g \|$$
What I really don't understand is how is computed $\sup_{g \in G} \inf_{f \in F} \| f - g \|$ also because if $F = \{ax | a \in \mathbb{R}\}$ I expect the value $\sup_{g \in G} \inf_{f \in F} \| f - g \|$ to be unbounded.