Second order rectifiability of varifolds of bounded mean curvature

We prove that the support of an $ m dimensional rectifiable varifold with a uniform lower bound on density and bounded generalized mean curvature can be covered \mathscr{H}^{m} almost everywhere by countable union $m$ submanifolds class \mathcal{C}^{2} $. obtain this result using notion arbitrary closed sets originally developed in stochastic geometry extending to our geometric setting techniques Trudinger theory viscosity solutions PDE's.