  We show that product Chebyshev polynomial meshes can be used, in a fully
discrete way, to evaluate with rigorous error bounds the Lebesgue constant,
i.e. the maximum of the Lebesgue function, for a class of polynomial projectors
on cube, simplex and ball, including interpolation, hyperinterpolation and
weighted least-squares. Several examples are presented and possible
generalizations outlined. A numerical software package implementing the method
is freely available online.
