Open Access
1995/1996 On Fubini-type theorems
Marek Balcerzak, Janusz Pawlikowski, Joanna Peredko
Author Affiliations +
Real Anal. Exchange 21(1): 340-344 (1995/1996).


We discuss some questions concerning the strengthened version of the Kuratowski-Ulam theorem obtained by Ceder. In particular, we refute Ceder’s conjecture that the measure analogue of his result holds. Further we consider mixed product \(\sigma\)-ideals \(\mathbb{K}\times \mathbb{L}\) and \(\mathbb{L}\times \mathbb{K}\) in \({\mathbb{R}}^2\) where \(\mathbb{K}\) and \(\mathbb{L}\) denote the families of meager and of Lebesgue null sets in \(\mathbb{R}\). For a set \(A\in \mathbb{K}\times \mathbb{L}\) (or \(A\in \mathbb{L} \times \mathbb{K}\)) we find large sets \(P\) and \(Q\) such that \(P\times Q\) misses \(A\). The proof is based on similar properties of \(\mathbb{K}\times\mathbb{K}\) and \(\mathbb{L}\times\mathbb{L}\) obtained by Ceder, Brodski\u i and Eggleston. A parametrized version of a Fubini-type theorem is also given.


Download Citation

Marek Balcerzak. Janusz Pawlikowski. Joanna Peredko. "On Fubini-type theorems." Real Anal. Exchange 21 (1) 340 - 344, 1995/1996.


Published: 1995/1996
First available in Project Euclid: 3 July 2012

zbMATH: 0857.28002
MathSciNet: MR1377546

Primary: 04A15 , 28A05

Keywords: Fubini theorem , meager set , null set , products of \(\sigma\)-ideal

Rights: Copyright © 1995 Michigan State University Press

Vol.21 • No. 1 • 1995/1996
Back to Top