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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2039815
Page Count: 4
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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.
Proceedings of the American Mathematical Society © 1975 American Mathematical Society