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Remarks on some generalization of the notion of microscopic sets

  • Aleksandra Karasińska EMAIL logo
From the journal Mathematica Slovaca

Abstract

We consider properties of defined earlier families of sets which are microscopic (small) in some sense. An equivalent definition of considered families is given, which is helpful in simplifying a proof of the fact that each Lebesgue null set belongs to one of these families. It is shown that families of sets microscopic in more general sense have properties analogous to the properties of the σ-ideal of classic microscopic sets.

MSC 2010: 28A05; 28A75

Acknowledgement

The author wishes to express her thanks to Professor W. Wilczyński for his helpful suggestions during the preparation of the paper.

  1. (Communicated by Tomasz Natkaniec)

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Received: 2019-11-26
Accepted: 2020-03-06
Published Online: 2020-12-10
Published in Print: 2020-12-16

© 2020 Mathematical Institute Slovak Academy of Sciences

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