Exceptional directions for Sierpiński's nonmeasurable sets

B. Kirchheim; Tomasz Natkaniec

Fundamenta Mathematicae (1992)

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


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


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

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},

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 -


  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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