Editing Moment problem (section)

== Uniqueness (or determinacy) ==
{{See also| Carleman's condition|Krein's condition}}
The uniqueness of <math>\mu</math> in the Hausdorff moment problem follows from the [[Weierstrass approximation theorem]], which states that [[polynomial]]s are [[dense set|dense]] under the [[uniform norm]] in the space of [[continuous functions]] on <math>[0,1]</math>. For the problem on an infinite interval, uniqueness is a more delicate question.{{sfn|Akhiezer|1965}} There are distributions, such as [[log-normal distribution]]s, which have finite moments for all the positive integers but where other distributions have the same moments.