  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
constant 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 WAMs. Our main results show that WAM's and their
stronger variant, admissible meshes, can be generated by random sampling, and
our analysis provides concrete estimates for growth of both the meshes and the
discrete-continuum comparability constants.
