On two theorems of Sierpiński

Edward Grzegorek , Iwo Labuda

Abstract

A theorem of Sierpiński says that every infinite set Q of reals contains an infinite number of disjoint subsets whose outer Lebesguemeasure 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.
Author Edward Grzegorek (FMPI / IM)
Edward Grzegorek,,
- Institute of Mathematics
, Iwo Labuda
Iwo Labuda,,
-
Journal seriesArchiv Der Mathematik, ISSN 0003-889X, (A 20 pkt)
Issue year2018
Vol110
No6
Pages637-644
Publication size in sheets0.5
Keywords in EnglishBaire category, Baire property, μ-measurability, measurable set, completely non-measurable set, full subset, outer measure, measurable envelope
DOIDOI:10.1007/s00013-018-1179-8
URL https://link.springer.com/content/pdf/10.1007%2Fs00013-018-1179-8.pdf
Languageen angielski
Score (nominal)20
ScoreMinisterial score = 20.0, ArticleFromJournal
Ministerial score (2013-2016) = 20.0, ArticleFromJournal
Publication indicators WoS Impact Factor: 2017 = 0.59 (2) - 2017=0.583 (5)
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