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Archiv der Mathematik

, Volume 110, Issue 6, pp 637–644 | Cite as

On two theorems of Sierpiński

  • Edward Grzegorek
  • Iwo Labuda
Article
  • 71 Downloads

Abstract

A theorem of Sierpiński says that every infinite set Q of reals contains an infinite number of disjoint subsets whose outer Lebesgue measure is the same as that of Q. He also has a similar theorem involving Baire property. We give a general theorem of this type and its corollaries, strengthening classical results.

Keywords

Baire category Baire property \(\mu \)-measurability Measurable set Completely non-measurable set Full subset Outer measure Measurable envelope 

Mathematics Subject Classification

28A05 54E52 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of GdańskGdańskPoland
  2. 2.Department of MathematicsThe University of MississippiUniversityUSA

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