A general fibre theorem for moment problems and some applications

The fibre theorem 12] for the moment problem on closed semi-algebraic subsets of R ^d is generalized to finitely generated real unital algebras. As an application two new theorems on the rational multidimensional moment problem are proved. Another application is a characterization of moment functionals on the polynomial algebra Rx ₁,..., x _d ] in terms of extensions. Finally, the fibre theorem and the extension theorem are used to reprove basic results on the complex moment problem due to Stochel and Szafraniec 13] and Bisgaard 2].