# PAC learnable bound with VC-dimension
Last edited: 2026-01-28
# Statement
Lemma
For a learner with a hypothesis space $H$ with VC dimension $VC(H)$, if we draw
$$m \geq \frac{1}{\epsilon} \left (8 \cdot VC(H) \cdot \log_2\left(\frac{13}{\epsilon}\right) + 4 \log_2\left(\frac{2}{\delta}\right) \right)$$i.i.d. samples for training data $T$ and there exists a hypothesis consistent with $T$, then this will be a PAC learner with $\leq \epsilon$ accuracy with probability $1-\delta$.