Glivenko-Cantelli

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In the theory of machine learning a concept class (hypothesis class) H is said to be Glivenko-Cantelli learnable, if $\forall \epsilon>0 \ \forall \delta > 0 \ \exists m_0 \in \mathbb{N} \ \forall m > m_0 \ \forall P \quad \Pr_{S \in P^m}\left[\forall h \in H \ |\mathrm{Err}^S(h) - \mathrm{Err}^P(h)| > \epsilon \right] < \delta$