0

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.

Sam
  • 357
  • 2
    If you pick some $g$, then $\inf_f |f-g|$ is a measure of how 'well' $f$ (or the functions in $F$, really) can approximate $g$. Then the $\sup_g$ finds the worst case. The resulting value (which may be infinite), is a measure of how well the functions in $F$ can approximate the functions in $G$ (where the norm is the measure of 'well'). Note that if $F =G$ then the result is zero, of course. – copper.hat Nov 18 '16 at 14:54
  • Now it's clear. Thanks – Sam Nov 18 '16 at 15:15

0 Answers0