# $\mu$-measurable >[!info] Definition >$\kappa$ is *$\mu$-measurable* if there is an elementary embedding $j:V\to M$, $\mathrm{crit}(j)=\kappa$, and if $U$ is the normal ultrafilter associated with $j$, then $U\in M$. >[!note] Remark >This is the weakest large cardinal property which requires the existence of [[Extenders|extenders]] which are not equivalet to normal [[ultrafilters]].