The notation $]a,b[$ is here meant to be the same thing as the open interval $(a,b)$. I believe this notation is meant to refer to the fact that $(a,b) = \\{ (-\infty,a] \cup [b,\infty)\\}^C$.
As for the $I_\lambda$ definition, it's hard to say for sure from just the two small pictures you've posted. For instance, it's not clear what $A$ and $E$ are and if / how they depends on any parameters. If I had to guess, though, I would say that there is a typo in the definition and the $\mu$ is supposed to be a $\lambda$, i.e. the infimum is taken over $u$ such that $|u|_{L^2}^2 = \lambda$.