  We extend the Jang equation proof of the positive energy theorem due to R.
Schoen and S.-T. Yau from dimension $n=3$ to dimensions $3 \leq n <8$. This
requires us to address several technical difficulties that are not present when
$n=3$. The regularity and decay assumptions for the initial data sets to which
our argument applies are weaker than those of R. Schoen and S.-T. Yau. In
recent joint work with L.-H. Huang, D. Lee, and R. Schoen we have given a
different proof of the full positive mass theorem in dimensions $3 \leq n < 8$.
We pointed out that this theorem can alternatively be derived from our density
argument and the positive energy theorem of the present paper.
