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Suppose <math>\mathcal H</math> is a class of real-valued functions with range in <math>[0,T]</math>. Then, <math>\mathcal H</math> is <math>(\epsilon,\delta)</math>-PAC-learnable with a sample of size:
<ref name=mr15>{{cite book|first1=Martin|last1=Anthony|first2=Peter L.|last2=Bartlett|title=Neural Network Learning: Theoretical Foundations|year=2009|isbn=9780521118620}}</ref><ref>{{cite conference|title=On the Pseudo-Dimension of Nearly Optimal Auctions|year=2015|conference=NIPS|url=http://papers.nips.cc/paper/5766-on-the-pseudo-dimension-of-nearly-optimal-auctions|arxiv=1506.03684|last1=Morgenstern|first1=Jamie|author1-link=Jamie Morgenstern|last2=Roughgarden|first2=Tim|pages=136–144|publisher=Curran Associates}}</ref>
<math display="block">
N = O\bigg(T^2\frac{PD(\mathcal H)\ln{T\over \epsilon} + \ln{1\over \delta}}{\epsilon^2}\bigg)
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