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Accessible Unlicensed Requires Authentication Published by De Gruyter October 20, 2018

On microscopic sets and Fubini Property in all directions

Adam Paszkiewicz
From the journal Mathematica Slovaca

Abstract

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.

  1. Communicated by David Buhagiar

Acknowledgement

The author would like to thank the paper’s reviewer, whose remarks have been substantial in obtaining the final version of the article.

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Received: 2016-11-25
Accepted: 2017-07-07
Published Online: 2018-10-20
Published in Print: 2018-10-25

© 2018 Mathematical Institute Slovak Academy of Sciences