The notion of a weak stability boundary has been successfully used to design
low energy trajectories from the Earth to the Moon. The structure of this
boundary has been investigated in a number of studies, where partial results
have been obtained. We propose a generalization of the weak stability boundary.
We prove analytically that, in the context of the planar circular restricted
three-body problem, under certain conditions on the mass ratio of the primaries
and on the energy, the weak stability boundary about the heavier primary
coincides with a branch of the global stable manifold of the Lyapunov orbit
about one of the Lagrange points