Jean Lasserre - Université de Toulouse III (Paul Sabatier), LAAS-CNRS Let « mu » be a Borel measure on a compact space Y \times X\times [0,1] whose marginal on X \times [0,1] is the Lebesgue measure. In addition assume that « mu » is supported on the graph { (y(x,t),x,t): (x,t) in X \times [0,1] } of a function (x,t) -> y(x,t), and we have only access to all moments of « mu » up to order 2d. We provide a new methodology to extract the function y from this moment-based information. It is based on the Christoffel function associated with « mu » and relatively simple to implement. One of its attractive features confirmed in preliminary experimental results is to strongly attenuate the Gibbs phenomenon usually inherent to methods that approximate y(x,t) with polynomials (e.g., typically the case when y is a discontinuous solution of some PDE). Joint work with D. Henrion, S. Marx, E. Pauwels and T. Weisser.