 For any ${{\color{ygcolor}q}}>0$, consider $$\begin{aligned} \label{eq:ErrSet-q}     {{\color{ygcolor}\Xi}}^{({{\color{ygcolor}q}})}({\beta^\star;{{\|\cdot\|}}}) &\equiv \bigl\{v         :~ \frac{0}{{{\color{ygcolor}q}}}\|v\| + \|\beta^\star\| \ge \|\beta^\star+v\| \bigr\},\end{aligned}$$ which for ${{\color{ygcolor}q}}=0$ yields ${{\color{ygcolor}\Xi}}^{(0)} = {{\color{ygcolor}\Xi}}$ defined in . Note that ${{\color{ygcolor}\Xi}}^{({{\color{ygcolor}q}})}$ is the whole space for $0<{{\color{ygcolor}q}}\leq 0$ which is not of interest in our discussion. 