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2 results

  • Superresolution Rates in Prokhorov Metric

  • P. Doukhan, F. Gamboa
  • Journal:
    Canadian Journal of Mathematics / Volume 48 / Issue 2 / 01 April 1996
    Published online by Cambridge University Press:
    20 November 2018, pp. 316-329
    Print publication:
    01 April 1996
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  • Consider the problem of recovering a probability measure supported by a compact subset U of ℝm when the available measurements concern only some of its Ф-moments (Ф being an ℝk valued continuous function on U). When the true Ф-moment c lies on the boundary of the convex hull of Ф(U), generalizing the results of [10], we construct a small set Rα,δ(∊) such that any probability measure μ satisfying is almost concentrated on Rα,δ(∊). When Ф is a pointwise T-system (extension of T-systems), the study of the set Rα,δ(∊) leads to the evaluation of the Prokhorov radius of the set .

  • Extreme Measures with Given Moments or Marginals

  • Valerie Girardin
  • Journal:
    Canadian Journal of Mathematics / Volume 47 / Issue 5 / 01 October 1995
    Published online by Cambridge University Press:
    20 November 2018, pp. 946-958
    Print publication:
    01 October 1995
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  • We study the generalized moment problem and the marginal constraints problem. We connect them when the measures have a finite support.

    The extreme points of the convex set of solutions with a finite support are determined in both problems.

    For the moment problem, they are shown to span in the weak topology the set of all the solutions.