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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A Gross measure property


Author: Lawrence R. Ernst
Journal: Trans. Amer. Math. Soc. 238 (1978), 397-406
MSC: Primary 28A75
MathSciNet review: 0476999
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Abstract: We prove that there exists a subset E of $ [0,1] \times {{\mathbf{R}}^2}$ such that the 2-dimensional Gross measure of E is 0, while the 1-dimensional Gross measure of $ \{ z:(y,z) \in E\} $ is positive for all $ y \in [0,1]$. It is known that for Hausdorff measures no set exists satisfying these conditions.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0476999-7
PII: S 0002-9947(1978)0476999-7
Keywords: Gross measure, Hausdorff measure, structure theory, $ ({\mathcal{G}^m},m)$ rectifiable
Article copyright: © Copyright 1978 American Mathematical Society