A new proof of the rectifiable slices theorem

This paper gives a new proof of the fact that a $k$-dimensional normal current $T$ in ${ℝ}^m$ is integer multiplicity rectifiable if and only if for every projection $P$ onto a $k$-dimensional subspace, almost every slice of $T$ by $P$ is $0$-dimensional integer multiplicity rectifiable, in other words, a sum of Dirac masses with integer weights. This is a special case of the Rectifiable Slices Theorem, which was first proved a few years ago by B. White.