  A weakly admissible mesh (WAM) on a continuum real-valued domain is a
sequence of discrete grids such that the discrete maximum norm of polynomials
on the grid is comparable to the supremum norm of polynomials on the domain.
The asymptotic rate of growth of the grid sizes and of the comparability
constants must grow in a controlled manner. In this paper, we generalize the
notion of a WAM to a hierarchical subspaces of not necessarily polynomial
functions, and we analyze particular strategies for random sampling as a
technique for generating WAM's. Our main results show that WAM's and their
stronger variant, admissible meshes (AM's), can be generated by random
sampling, and our analysis provides concrete estimates for growth of both the
meshes and the discrete-continuum comparability constants.
