<abstract xmlns="http://www.w3.org/1999/xhtml"> In 2000, I. Recław and P. Zakrzewski introduced the notion of Fubini Property for the pair (I,J) of two σ-ideals in the following way. Let I and J be two σ-ideals on Polish spaces X and Y, respectively. The pair (I,J) has the Fubini Property (FP) if for every Borel subset B of X×Y such that all its vertical sections Bx = {y ∈ Y : (x, y) ∈ B} are in J, then the set of all y ∈ Y, for which horizontal section By = {x ∈ X : (x, y) ∈ B} does not belong to I, is a set from J, i.e., {y ∈ Y : By ∉ I} ∈ J. The Fubini property for the σ-ideal M of microscopic sets is considered and the proof that the pair (M,M) does not satisfy (FP) is given.</abstract>

In 2000, I. Recław and P. Zakrzewski introduced the notion of Fubini Property for the pair (I,J) of two σ-ideals in the following way. Let I and J be two σ-ideals on Polish spaces X and Y, respectively. The pair (I,J) has the Fubini Property (FP) if for every Borel subset B of X×Y such that all its vertical sections Bx = {y ∈ Y : (x, y) ∈ B} are in J, then the set of all y ∈ Y, for which horizontal section By = {x ∈ X : (x, y) ∈ B} does not belong to I, is a set from J, i.e., {y ∈ Y : By ∉ I} ∈ J. The Fubini property for the σ-ideal M of microscopic sets is considered and the proof that the pair (M,M) does not satisfy (FP) is given.

Fubini Property for Microscopic Sets

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{"article-title":"Fubini Property for Microscopic Sets"}

In 2000, I. Recław and P. Zakrzewski introduced the notion of Fubini Property for the pair (I,J) of two σ-ideals in the following way. Let I and J be two...

Fubini Property for Microscopic Sets

Online veröffentlicht: 04. Aug. 2016

Seitenbereich: 143 - 149

Eingereicht: 18. Nov. 2015

DOI: https://doi.org/10.1515/tmmp-2016-0012

Schlüsselwörter
sets of Lebesgue measure zero, sets of the first category, microscopic sets on the plane, Fubini Theorem, Fubini property

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Fubini Property for Microscopic Sets

Online veröffentlicht: 04. Aug. 2016

Seitenbereich: 143 - 149

Eingereicht: 18. Nov. 2015

DOI: https://doi.org/10.1515/tmmp-2016-0012

Schlüsselwörtersets of Lebesgue measure zero, sets of the first category, microscopic sets on the plane, Fubini Theorem, Fubini property

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Schlüsselwörter
sets of Lebesgue measure zero, sets of the first category, microscopic sets on the plane, Fubini Theorem, Fubini property