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.
@article{bwmeta1.element.bwnjournal-article-fmv140i3p237bwm,
author = {B. Kirchheim and Tomasz Natkaniec},
title = {Exceptional directions for Sierpi\'nski's nonmeasurable sets},
journal = {Fundamenta Mathematicae},
volume = {141},
year = {1992},
pages = {237-245},
zbl = {0757.28003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv140i3p237bwm}
}
Kirchheim, B.; Natkaniec, Tomasz. Exceptional directions for Sierpiński's nonmeasurable sets. Fundamenta Mathematicae, Tome 141 (1992) pp. 237-245. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv140i3p237bwm/
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