A proof that $\mathcal {H}^2$ and $\mathcal {T}^2$ are distinct measures
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- by Lawrence R. Ernst PDF
- Trans. Amer. Math. Soc. 191 (1974), 363-372 Request permission
Abstract:
It is proven that there exists a subset E of ${{\mathbf {R}}^3}$ such that the two-dimensional $\mathcal {J}$ measure of E is less than its two-dimensional Hausdorff measure. E is the image under the usual isomorphism of ${\mathbf {R}} \times {{\mathbf {R}}^2}$ onto ${{\mathbf {R}}^3}$ of the Cartesian product of $\{ x: - 4 \leq x \leq 4\}$ and a Cantor type subset of ${{\mathbf {R}}^2}$; the latter term in this product is the intersection of a decreasing sequence, every member of which is the union of certain closed circular disks.References
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Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 191 (1974), 363-372
- MSC: Primary 28A75
- DOI: https://doi.org/10.1090/S0002-9947-1974-0361007-5
- MathSciNet review: 0361007