Eventual Capture on a Measurable Cardinal

We continue the study from \cite{BrendleFreidmanMontoya, vandervlugtlocalizationcardinals} of localization cardinals ${\text{mfb}}_{\kappa }({\in }^{\ast })$ and ${\text{mfd}}_{\kappa }({\in }^{\ast })$ and their variants at regular uncountable $\kappa$. We prove that if $\kappa$ is measurable then these cardinals trivialize. We also provide other fundamental restrictions in the most general setting. We prove the results are optimal by forcing different values for ${\mathfrak{b}}_{{\text{id}}^{+}}({\in }^{\ast }),{\mathfrak{d}}_{{\text{id}}^{++}}({\in }^{\ast })$ at a measurable. As a by-product, we prove the consistency of ${\text{mfb}}_h({\in }^{\ast })<{\text{mfb}}_{h^{\mathrm{\prime }}}({\in }^{\ast })$ for functions $h,h^{\mathrm{\prime }}\in \text{kk}$, thus answering a question of Brendle, Brooke-Taylor, Friedman and Montoya. Moreover, we study the relation between these cardinals and other well-known cardinal invariants.