Exceptional directions for Sierpiński's nonmeasurable sets

B. Kirchheim; Tomasz Natkaniec

Fundamenta Mathematicae (1992)

  • Volume: 140, Issue: 3, page 237-245
  • ISSN: 0016-2736

Abstract

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In [2] the question was considered in how many directions can a nonmeasurable plane set behave even "better" than the classical one constructed by Sierpiński in [6], in the sense that any line in a given direction intersects the set in at most one point. We considerably improve these results and give a much sharper estimate for the size of the sets of those "better" directions.

How to cite

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Kirchheim, B., and Natkaniec, Tomasz. "Exceptional directions for Sierpiński's nonmeasurable sets." Fundamenta Mathematicae 140.3 (1992): 237-245. <http://eudml.org/doc/211943>.

@article{Kirchheim1992,
author = {Kirchheim, B., Natkaniec, Tomasz},
journal = {Fundamenta Mathematicae},
keywords = {Sierpiński’s nonmeasurable sets; Lebesgue measurability; Borel sets; nonprojective sets; sections; Baire property},
language = {eng},
number = {3},
pages = {237-245},
title = {Exceptional directions for Sierpiński's nonmeasurable sets},
url = {http://eudml.org/doc/211943},
volume = {140},
year = {1992},
}

TY - JOUR
AU - Kirchheim, B.
AU - Natkaniec, Tomasz
TI - Exceptional directions for Sierpiński's nonmeasurable sets
JO - Fundamenta Mathematicae
PY - 1992
VL - 140
IS - 3
SP - 237
EP - 245
LA - eng
KW - Sierpiński’s nonmeasurable sets; Lebesgue measurability; Borel sets; nonprojective sets; sections; Baire property
UR - http://eudml.org/doc/211943
ER -

References

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  1. [1] D. L. Cohn, Measure Theory, Birkhäuser, 1980. 
  2. [2] M. Frantz, On Sierpiński's nonmeasurable set, Fund. Math. 139 (1991), 17-22. Zbl0757.28002
  3. [3] A. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), 93-114. Zbl0472.03040
  4. [4] J. Oxtoby, Measure and Category, Springer, 1971. 
  5. [5] J. Shoenfield, Martin's Axiom, Amer. Math. Monthly 82 (1975), 610-617. Zbl0314.02069
  6. [6] W. Sierpiński, Sur un problème concernant les ensembles mesurables superficiellement, Fund. Math. 1 (1920), 112-115. Zbl47.0180.04
  7. [7] U. Tricot, Two definitions of fractional dimension, Math. Proc. Cambridge Philos. Soc. 91 (1982), 57-75. 

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