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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A Gross measure property
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by Lawrence R. Ernst PDF
Trans. Amer. Math. Soc. 238 (1978), 397-406 Request permission

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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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 238 (1978), 397-406
  • MSC: Primary 28A75
  • DOI: https://doi.org/10.1090/S0002-9947-1978-0476999-7
  • MathSciNet review: 0476999