A positive mass theorem for asymptotically flat manifolds with a non-compact boundary

We define a mass-type invariant for n-dimensional asymptotically flat manifolds with a non-compact boundary and prove a positive mass theorem if either 3 <= n <= 7 or if n >= 3 and the manifold is spin. This settles, for this class of manifolds, a question posed in a recent paper by the first author in connection with the long-term behavior of a certain Yamabe-type flow on scalar-flat compact manifolds with boundary.