A Gross Measure Property

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1978Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 238, page 397 (issn: 0002-9947,

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Authors: Ernst, Lawrence R.;

doi: 10.2307/1997815 , 10.1090/s0002-9947-1978-0476999-7

A Gross Measure Property

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Abstract

We prove that there exists a subset E of [ 0 , 1 ] × R 2 [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 ) ∈ E } \{ z:(y,z) \in E\} is positive for all y ∈ [ 0 , 1 ] y \in [0,1] . It is known that for Hausdorff measures no set exists satisfying these conditions.

Related Organizations

City University of New York
United States
Queens College, CUNY
United States

Keywords

Length, area, volume, other geometric measure theory, Measures and integrals in product spaces

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