SUPERRESOLUTION RATES IN PROKHOROV METRIC

Consider the problem of recovering a probability measure supported by a compact subset U of R(m) when the available measurements concern onl y some of its phi-moments (phi, being an R(k) valued continuous functi on on U). When the true phi-moment c lies on the boundary of the conve x hull of phi(U), generalizing the results of [10], we construct a sma ll set R(alpha delta(epsilon)) such that any probability measure mu sa tisfying \\integral(U) phi(x)d mu(x)-c\\ less than or equal to epsilon is almost concentrated on R(alpha delta(epsilon)). When phi is a poin twise T-system (extension of T-systems), the study of the set R(alpha delta(epsilon)) leads to the evaluation of the Prokhorov radius of the set {mu : \\integral(U) phi(x)d mu(x) - c\\ less than or equal to eps ilon}.