SUPERRESOLUTION RATES IN PROKHOROV METRIC

Consider the problem of recovering a probability measure supported by the compact set [0, 1], when the available measurements concern only s ome of its PHI-moments (PHI being an R(k) valued continuous function o n [0, 1]). When the true PHI-moment c lies on the boundary of the conv ex hull of PHI ([0, 1]), generalizing the results of [3], we construct a small Lebesgue measure set R(alpha, delta, (epsilon)) such that any probability measure A satisfying parallel-to integral[0, 1] PHI (x) d mu (x) - c parallel-to epsilon is almost concentrated on R(alpha, delt a (epsilon). When PHI is assumed to be a punctual T-system, the descri ption of R(alpha, delta (epsilon) allows the evaluation of the Prokhor ov radius of the set {mu : parallel-to integral[0, 1] PI (x) dmu (x) - c parallel-to less-than-or-equal-to epsilon}.