  Brakke flow is defined with a variational inequality, which means it may have
discontinuous mass over time, i.e. have mass drop. It has long been conjectured
that the Brakke flow associated to a nonfattening level set flow has no mass
drop and achieves equality in the Brakke inequality. Under natural assumptions,
we show that a flow has no mass drop if and only if it satisfies the
multiplicity one conjecture $\mathcal{H}^n$-a.e. One application is that there
is no mass drop for level set flows with mean convex neighborhoods of
singularities, and a generic flow has no mass drop until there is a higher
multiplicity planar tangent flow. Also, if a nonfattening flow has no higher
multiplicity planes as limit flows, then each limit flow has no mass drop. We
upgrade these results to equality in the Brakke inequality for certain
important cases. We show that nonfattening flows with three-convex blow-up type
are Brakke flows with equality. This includes flows with generic singularities
in dimension three and flows with mean convex neighborhoods of singularities in
dimension four.
