We know that Carleman's condition is a sufficient condition for the determinacy of Hamburger moment problem and the Stieltje's moment problem. The first one look at measures on the real line, and the second one look at measures on the positive side of the real line.
There is a third problem called Hausdorff moment problem that looks at measures on the bounded interval. The interesting thing about this problem is that if the measure that fits moments exists, it is also unique.
My question: Is Carleman's condition also sufficient for the determinacy of the Hausdorff moment problem? I figure that it should be since Hausdorff moment problem looks at smaller set of distribution than the Hamburger moment problem.
I looked around but I couldn't really find this anywhere. I just want to makesure that I am not missing something subtle.