Exceptional directions for Sierpiński's nonmeasurable sets

Volume 140 / 1992

B. Kirchheim, Tomasz Natkaniec Fundamenta Mathematicae 140 (1992), 237-245 DOI: 10.4064/fm-140-3-237-245


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.


  • B. Kirchheim
  • Tomasz Natkaniec

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