� Measure of Cartesian Product Sets

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 May 1975Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 49, page 199 (issn: 0002-9939,

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Authors: Lawrence R. Ernst;

doi: 10.2307/2039815 , 10.1090/s0002-9939-1975-0367162-1

� Measure of Cartesian Product Sets

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Abstract

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