Let f be a function from Rp to Rq and let A be a finite set of pairs (θ, η) ϵ Rp × Rq. Assume that the real-valued function η, f(x) is Lipschitz continuous in the direction θ for every (θ, η) ϵ Λ.

It is shown how to construct Lipschitz constants and moduli of continuity for the Chebyshev projection of $C\lbrack 0, 1 \rbrack$ onto the finite-dimensional subspace ...