Dual pairs of Riesz spaces for studying completeness, sufficiency, and compactness of statistical experiments

For statistical experiments dual pairs of Riesz spaces are introduced which are related to spaces defined by Pitcher in connection with compact experiments. Likewise there are relations to enlargements of Le Cam's M-space defined by Torgersen in a study on complete sufficient statistics and uniformly minimum variance unbiased estimators. In this framework completeness, (pairwise) sufficiency, and compactness are investigated. The results are applicable to nondominated experiments, for example, to show minimal sufficiency and completeness of permutation invariant sub-[sigma]-algebras. The relation to Le Cam's L- and M-spaces is indicated.