Fubini properties of ideals
Let \(\mathcal I\) and \(\mathcal J\) be \(\sigma\)-ideals on Polish spaces \(X\) and \(Y\), respectively. A pair \(({\mathcal I},{\mathcal J})\) has the Fubini Property if for every Borel set \(B\subset X\times Y\), if all its \(x\)-sections belong to \(\mathcal J\) then \(\{ y\in Y\colon B^y\not\in{\mathcal I}\}\in{\mathcal J}\). The authors consider the question which pairs of \(\sigma\)-ideals have the Fubini Property. A typical result: If \(\mathcal I\) and \(\mathcal J\) are \(\Sigma_2^{0}\) supported and \(\mathcal I\) is ccc then the pair \(({\mathcal I},{\mathcal J})\) satisfies FP.
scientific article; zbMATH DE number 1848781