  This paper is concerned with uniform measure estimates for nodal sets of
solutions in elliptic homogenization. We consider a family of second-order
elliptic operators $\{ \mathcal{L}_\e\}$ in divergence form with rapidly
oscillating and periodic coefficients. We show that the $(d-1)$-dimensional
Hausdorff measures of the nodal sets of solutions to $\mathcal{L}_\e (u_\e)=0$
in a ball in $\R^d$ are bounded uniformly in $\e>0$. The proof relies on a
uniform doubling condition and approximation of $u_\e$ by solutions of the
homogenized equation.
