We are asked to show that
- $B$ is the domain of $Q$ and is compact
- $Q(\beta)$ is continuous in $\beta$
- $Q(\beta)$ is uniquely minimized at $\beta_0$
implies
$\forall \epsilon >0 \; \exists \delta>0 : \underset{||\beta - \beta_0||>\epsilon}{\inf} Q(\beta) \geq Q(\beta_0) + \delta$.
Why do I need conditions 1. and 2. ? Am I not immediately finished using condition 3.?