Fubini properties of ideals
type: Item
instance of: scholarly article
title: Fubini properties of ideals
zbMATH Open document ID: 1016.03050
author: Ireneusz Recław
author: P. Zakrzewski
published in: Real Analysis Exchange
publication date: 2003-01-05T00:00:00Z
review text: 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.
reviewed by: Tomasz Natkaniec
Mathematics Subject Classification ID: 03E15
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 28A05
zbMATH DE Number: 1848781
zbMATH Keywords: Polish space
zbMATH Keywords: Fubini property
zbMATH Keywords: \(\sigma\)-ideals
zbMATH Keywords: Borel sets
zbMATH Keywords: ccc ideals
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1848781