TITLE: Given $(x_n)$, does there exist a measure such that $x_n=\int_0^1t^n d\mu$?
QUESTION [6 upvotes]: Let $(x_n)$ be a sequence of real numbers. Does there exist a measure $\mu$ on $[0,1]$ such that $x_n=\int\limits_0^1t^nd\mu$ ?

REPLY [3 votes]: This is the Hausdorff moment problem.  Here is a reference: http://en.wikipedia.org/wiki/Hausdorff_moment_problem.