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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

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Volume 68, Issue 5


On microscopic sets and Fubini Property in all directions

Adam Paszkiewicz
Published Online: 2018-10-20 | DOI: https://doi.org/10.1515/ms-2017-0165


For the σ-ideal N of nullsets and σ-ideal M of microscopic sets, it was recently obtained that there exists a Borel set E2 with the following property: ExM for any x and {y;EyN}M, for vertical sections Ex={y;(x,y)E} and horizontal sections Ey={x;(x,y)E} for E2. Thus (N,M) does not satisfy Fubini Property. In this paper we obtain such Borel set E, that {y;EyN}M and all non-horizontal (in a natural sense) sections of E are in M. Other Fubini type properties, with conditions written for all directions are also discussed.

MSC 2010: Primary 28A05; Secondary 03E15; 26A30

Keywords: nullsets; microscopic sets; Fubini property; marginal distributions


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About the article

Received: 2016-11-25

Accepted: 2017-07-07

Published Online: 2018-10-20

Published in Print: 2018-10-25

Communicated by David Buhagiar

Citation Information: Mathematica Slovaca, Volume 68, Issue 5, Pages 1041–1048, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2017-0165.

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