We answer a question posed by Ilmanen on the integrality of varifolds which appear as the singularperturbation limit of the Allen-Cahn equation. We show that the density of the limit measure isinteger multiple of the surface constant almost everywhere at almostall time. This shows that limit measures obtained via the Allen-Chanequation and those via Brakke's construction share the same integralityproperty as well as being weak solutions for the mean curvature flow equation.
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