  We prove convergence of Hausdorff measure of level sets of smooth Gaussian
fields when the levels converge. Given two coupled stationary fields $f_1, f_2$
, we estimate the difference of Hausdorff measure of level sets in expectation,
in terms of $C^2$-fluctuations of the field $F=f_1-f_2$. The main idea in the
proof is to represent difference in volume as an integral of mean curvature
using the divergence theorem.
  This approach is different from using Kac-Rice type formula as main tool in
the analysis.
