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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ T$ measure of Cartesian product sets. II


Author: Lawrence R. Ernst
Journal: Trans. Amer. Math. Soc. 222 (1976), 211-220
MSC: Primary 28A75
MathSciNet review: 0422587
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Abstract: It is proven that there exists a subset A of Euclidean 2-space such that the 2-dimensional T measure of the Cartesian product of an interval of unit length and A is less than the 1-dimensional T measure of A. In a previous paper it was shown that there exists a subset of Euclidean 2-space such that the reverse inequality holds. T measure is the first measure of its type for which it has been shown that both of these relations are possible.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1976-0422587-6
PII: S 0002-9947(1976)0422587-6
Keywords: 1-dimensional measures, 2-dimensional measures, Cartesian product sets, T measure, Hausdorff measure, Carathéodory measure
Article copyright: © Copyright 1976 American Mathematical Society