In mathematics, Carleman's condition is a sufficient condition for the determinacy of the moment problem.

Hamburger moment problem

For the Hamburger moment problem, the theorem, proved by Torsten Carleman

Torsten Carleman

Torsten Carleman , born Tage Gills Torsten Carleman, was a Swedish mathematician....

, states the following:

Let μ be a measure

Measure (mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, and volume...

 on R such that all the moments


are finite. If
then the moment problem for m_n is determinate; that is, μ is the only measure on R with (m_n) as its sequence of moments.

Stieltjes moment problem

For the Stieltjes moment problem, the sufficient condition for determinacy is