  In 'Tractable semi-algebraic approximation using Christoffel-Darboux kernel'
Marx, Pauwels, Weisser, Henrion and Lasserre conjectured, that the
approximation rate $\mathcal O(\frac 1 {\sqrt(d)})$ of a Lipschitz functions by
a semi-algebraic function induced by a Christoffel- Darboux kernel of degree
$d$ in the $L^1$ norm can be improved for more regular functions. Here we will
show, that for semi-algebraic and definable functions the results can be
strengthened to a rational approximation rate in the $L^\infty$ norm.
