Consider an ensemble classifier constructed by T rounds of AdaBoost on N training examples. \begin{align} H(\mathbf{x}) = \sum_{t= 1}^{T} \alpha_{t} h_{t}(\mathbf{x}) \end{align}
The next classifier: $h_{T+1}$ is added to the ensemble, by minimizing the training error weighted by $W_{1}^{T}$ ... $W_{N}^{T}$. For the question, I am trying to figure out how to show that $$\epsilon_{T + 1}$$ (the training error of $h_{T+1}$) weighted by the updated weights $W_{1}^{T+1}$ ... $W_{N}^{T+1}$ equals $\frac{1}{2}$.