measure of Cartesian product sets. II

Author:
Lawrence R. Ernst

Journal:
Trans. Amer. Math. Soc. **222** (1976), 211-220

MSC:
Primary 28A75

DOI:
https://doi.org/10.1090/S0002-9947-1976-0422587-6

MathSciNet review:
0422587

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-1976-0422587-6

Keywords:
1-dimensional measures,
2-dimensional measures,
Cartesian product sets,
*T* measure,
Hausdorff measure,
Carathéodory measure

Article copyright:
© Copyright 1976
American Mathematical Society