On products of admissible liftings and densities
In Section 2, the class of admissible densities is introduced and studied. The main result in that section, Theorem 2.5, states that if \(\{(\Omega_i,\Sigma _i,\mu_i)\}_{i\in I}\) is a family of probability spaces with product \((\Omega,\Sigma,\mu)\), then for any fixed \(i_0\in I\) and for each density \(\tau _{i_0}\) (on \((\Omega,\Sigma,\mu_{i_0})\)) and for arbitrary admissible density \(\tau_i\) (on \((\Omega,\Sigma,\mu_i)\)) with \(i\in I\setminus \{i_{0}\}\) there exists a density \(\varphi\) (on \((\Omega,\Sigma,\mu)\)) such that \(\varphi\) respects coordinates, and \(\varphi\in\otimes_{i_0\in I}\tau_i\). This statement improves the corresponding result for product densities of \textit{N. D. Macheras} and \textit{W. Strauss} [Z. Anal. Anwend. 14, No. 1, 25-32 (1995; Zbl 0816.28006)] and implies the D. H. Fremlin's existence results for densities respecting coordinates. In Section 3, the class of admissibly generated liftings is introduced. This class let the authors to improve several results on product liftings and liftings respecting coordinates and also to provide them a unifying approach.
scientific article; zbMATH DE number 1356401