= VC uniform convergence theorem
{c}
{title2=$\sup_{h\in H}|\widehat R_m(h)-R(h)|\leq\eta$}
A finite <VC dimension> gives simultaneous control of <empirical misclassification risk> for every member of a <hypothesis class>. Sufficient independent sample size is $A\eta^{-2}(v\log(2/\eta)+\log(2/\delta))$. The displayed event implies an <empirical risk minimization> rule has <misclassification risk> at most $\inf_h R(h)+2\eta$, including for unrealizable labels.<Learnability and VC Dimension in MIT 6.790>[Uniform convergence and quantitative fundamental theorem]{ref}
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