Moment problems in an infinite number of variables

Abstract

Let ${ℝ}^{\infty }={\times }_{d=1}^{\infty }ℝ$. Given a closed set $K\subseteq {ℝ}^{\infty }$ and $s:S_{\ast }\to ℝ$, where $S_{\ast }$ denotes the set of tuples of nonnegative integers $(n_1,n_2,\dots )$ with $n_d>0$ for finitely many $d$, the $K$-moment problem on ${ℝ}^{\infty }$ entails determining whether or not there exists a measure $\sigma$ on ${ℝ}^{\infty }$ so that $\mathrm{\text{supp}}\sigma \subseteq K$ and