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On two theorems of Sierpiński

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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.

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Authors and Affiliations

  1. Institute of Mathematics, University of Gdańsk, Wita Stwosza 57, 80-308, Gdańsk, Poland

    Edward Grzegorek

  2. Department of Mathematics, The University of Mississippi, University, MS, 38677, USA

    Iwo Labuda

Authors
  1. Edward Grzegorek
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  2. Iwo Labuda
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Correspondence to Iwo Labuda.

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Grzegorek, E., Labuda, I. On two theorems of Sierpiński. Arch. Math. 110, 637–644 (2018). https://doi.org/10.1007/s00013-018-1179-8

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  • DOI: https://doi.org/10.1007/s00013-018-1179-8

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