𝑇 measure of Cartesian product sets. II

Ernst, Lawrence R.

doi:10.1090/S0002-9947-1976-0422587-6

$T$ measure of Cartesian product sets. II
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Trans. Amer. Math. Soc. 222 (1976), 211-220 Request permission

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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