measure of Cartesian product sets

Author:
Lawrence R. Ernst

Journal:
Proc. Amer. Math. Soc. **49** (1975), 199-202

MSC:
Primary 28A75

DOI:
https://doi.org/10.1090/S0002-9939-1975-0367162-1

MathSciNet review:
0367162

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Abstract | References | Similar Articles | Additional Information

Abstract: It is proven that there exists a subset of Euclidean -space such that the -dimensional measure of the Cartesian product of an interval of unit length and is greater than the -dimensional measure of . This shows that measure does not extend to Euclidean -space the relation that area is the product of length by length. As corollaries, new proofs of some related but previously known results are obtained.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1975-0367162-1

Keywords:
-dimensional measures,
-dimensional measures,
Cartesian product sets,
measure,
Hausdorff measure,
spherical measure,
Carathéodory measure

Article copyright:
© Copyright 1975
American Mathematical Society