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Microscopic and strongly microscopic sets on the plane. Fubini theorem and Fubini property

Karasińska A., Wagner-Bojakowska E.

Demonstratio Mathematica

2014

Vol. 47, nr 3

581--594

In this paper, we introduce the notions of microscopic and strongly microscopic sets on the plane and obtain a result analogous to Fubini Theorem.

On the uniqueness of measure and category σ-ideals on 2ω

Zakrzewski P.

Journal of Applied Analysis

2007

Vol. 13, nr 2

249-257

We prove that if of ccc, translation invariant σ-ideals on 2^{ω has the Fubini Property, then I = J. This leads to a slightly impoved exposition of a part of the Farah-Zapletal proof of an invariant version of their theorem which characterizes the measure and category σ-ideals on 2^{ω as essentially the only ccc definable σ-ideals with Fubini Property.}}