The Lie group of isometries of a pseudo-Riemannian manifold

We give an elementary proof of the Myers-Steenrod theorem, stat-ing that the group of isometries of a connected Riemannian man-ifold M is a Lie group acting smoothly on M. Our proof follows the approach of Chu and Kobayashi, but replacing their use of a theorem of Palais with a topological condition detecting when a locally compact subspace of M is an embedded integral manifold of a given k-plane distribution.