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Some results connected with a problem of Erdős. II


Author: Harry I. Miller
Journal: Proc. Amer. Math. Soc. 75 (1979), 265-268
MSC: Primary 28A05; Secondary 26A21
DOI: https://doi.org/10.1090/S0002-9939-1979-0532148-4
MathSciNet review: 532148
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Abstract: It is shown, using the continuum hypothesis, that if E is an uncountable subset of the real line, then there exist subsets $ {S_1}$ and $ {S_2}$ of the unit interval, such that $ {S_1}$ has outer Lebesgue measure one and $ {S_2}$ is of the second Baire category and such that neither $ {S_1}$ nor $ {S_2}$ contains a subset similar (in the sense of elementary geometry) to E. These results are related to a conjecture of P. Erdős.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0532148-4
Article copyright: © Copyright 1979 American Mathematical Society