  We define new norms for symmetric tensors over ordered normed spaces; these
norms are defined by considering linear combinations of tensor products or
powers of positive elements only. Relations between the different norms are
studied. The results are applied to the problem of representing a finitely
exchangeable distribution as a mixture of powers, i.e, mixture of distributions
of i.i.d. sequences, using a signed mixing measure.

Functional Analysis;Probability