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ℑ Measure of Cartesian Product Sets

Lawrence R. Ernst
Proceedings of the American Mathematical Society
Vol. 49, No. 1 (May, 1975), pp. 199-202
DOI: 10.2307/2039815
Stable URL: http://www.jstor.org/stable/2039815
Page Count: 4
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ℑ Measure of Cartesian Product Sets
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Abstract

It is proven that there exists a subset A of Euclidean 2-space such that the 2-dimensional J measure of the Cartesian product of an interval of unit length and A is greater than the 1-dimensional J measure of A. This shows that J measure does not extend to Euclidean 3-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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