ArticleOriginal scientific text
Title
Exceptional directions for Sierpiński's nonmeasurable sets
Authors 1, 2
Affiliations
- Institute of Applied Mathematics, Comenius University, Mlynská Dolina, 84215 Bratislava, Czechoslovakia
- Institute of Mathematics, WSP, Chodkiewicza 30, 85-064 Bydgoszcz, Poland
Abstract
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.
Bibliography
- D. L. Cohn, Measure Theory, Birkhäuser, 1980.
- M. Frantz, On Sierpiński's nonmeasurable set, Fund. Math. 139 (1991), 17-22.
- A. Miller, Some properties of measure and category, Trans. Amer. Math. Soc. 266 (1981), 93-114.
- J. Oxtoby, Measure and Category, Springer, 1971.
- J. Shoenfield, Martin's Axiom, Amer. Math. Monthly 82 (1975), 610-617.
- W. Sierpiński, Sur un problème concernant les ensembles mesurables superficiellement, Fund. Math. 1 (1920), 112-115.
- U. Tricot, Two definitions of fractional dimension, Math. Proc. Cambridge Philos. Soc. 91 (1982), 57-75.
Additional information
http://matwbn.icm.edu.pl/ksiazki/fm/fm140/fm14033.pdf
Pages:
237-245
Main language of publication
English
Received
1991-06-17
Published
1992
Exact and natural sciences