Abstract
The Hausdorff, Hamburger and Stieltjes moment problem and the sequence of maximum entropy (MaxEnt) approx- imates with given moments are considered. Thanks to MaxEnt formalism it is proved, through a unified procedure, MaxEnt approximate converges in entropy to the unknown distribution when the Hausdorff, Hamburger or Stieltjes moment problem are determinate and the underlying distribution has finite or (minus) infinite entropy.
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