A Gross measure property
HTML articles powered by AMS MathViewer
- 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.References
- Herbert Federer, Geometric measure theory, Die Grundlehren der mathematischen Wissenschaften, Band 153, Springer-Verlag New York, Inc., New York, 1969. MR 0257325
- D. J. Ward, A counter-example in area theory, Proc. Cambridge Philos. Soc. 60 (1964), 821–845. MR 170997, DOI 10.1017/S0305004100038317
- Hassler Whitney, Geometric integration theory, Princeton University Press, Princeton, N. J., 1957. MR 0087148, DOI 10.1515/9781400877577
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