## Real Analysis Exchange

### On Fubini-type theorems

#### Abstract

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.

#### Article information

Source
Real Anal. Exchange, Volume 21, Number 1 (1995), 340-344.

Dates
First available in Project Euclid: 3 July 2012

https://projecteuclid.org/euclid.rae/1341343252

Mathematical Reviews number (MathSciNet)
MR1377546

Zentralblatt MATH identifier
0857.28002

#### Citation

Balcerzak, Marek; Peredko, Joanna; Pawlikowski, Janusz. On Fubini-type theorems. Real Anal. Exchange 21 (1995), no. 1, 340--344. https://projecteuclid.org/euclid.rae/1341343252

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