  In this paper, we obtain the upper bounds for the Hausdorff measures of nodal
sets of eigenfunctions with the Robin boundary conditions, i.e.,
  \begin{equation*} {\left\{\begin{array}{l}
  \triangle u+\lambda u=0,\quad in\quad \Omega,\\ u_{\nu}+\mu u=0,\quad
on\quad\partial\Omega, \end{array} \right.} \end{equation*} where the domain
$\Omega\subseteq\mathbb{R}^n$, $u_{\nu}$ means the derivative of $u$ along the
outer normal direction of $\partial\Omega$. We show that, if $\Omega$ is
bounded and analytic, and the corresponding eigenvalue $\lambda$ is large
enough,then the measure upper bounds for the nodal sets of eigenfunctions are
$C\sqrt{\lambda}$, where $C$ is a positive constant depending only on $n$ and
$\Omega$ but not on $\mu$ We also show that, if $\partial\Omega$ is
$C^{\infty}$ smooth and $\partial\Omega\setminus\Gamma$ is piecewise analytic,
where $\Gamma\subseteq\partial\Omega$ is a union of some $n-2$ dimensional
submanifolds of $\partial\Omega$, $\mu>0$, and $\lambda$ is large enough, then
the corresponding measure upper bounds for the nodal sets of $u$ are
$C(\sqrt{\lambda}+\mu^{\alpha}+\mu^{-c\alpha})$ for some positive number
$\alpha$, where $c$ is a positive constant depending only on $n$, and $C$ is a
positive constant depending on $n$, $\Omega$, $\Gamma$ and $\alpha$.
