measure estimate of (\[e:haus\_est\]) is the first which gives an [*effective*]{} bound for the $n-2$ Hausdorff measure of the critical and singular sets, while of course the Minkowski estimate of (\[e:mink\_est\]) is in fact significantly stronger. As was previously discussed, under the assumption of Lipschitz coefficients the Hausdorff estimate (\[e:haus\_est\]) is the first to give that the $n-2$-Hausdorff measure is even finite. In fact, the techniques even show that the critical and singular sets are [*finitely*]{} rectifiable. That is, away from a set of $n-2$-measure zero we have that ${\mathcal{CS}}(u)$ is the finite union of biLipschitz images of subsets of ${\mathds{R}}^{n-2}$. On a manifold the constant $C$ should also depend on the sectional curvature bound of the manifold.

#### Main Results for Nodal Sets:

By a simple adaptation of the arguments used for critical sets, we are able to also give estimates on the [*nodal*]{} set of solutions $u$ to . In this case our effective Hausdorff estimates match those that are currently in the literature, however we do prove the significantly stronger Minkowski versions as well, which is quite new. To state the results let us recall the definition of the nodal and [*effective*]{} nodal sets given by $$\begin{aligned}
