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Families of surfaces lying in a null set

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

Laura Wisewell
Laura Wisewell
Affiliation:
School of Mathematics, University of Edinburgh, King–s Buildings, Edinburgh, EH9 3JZ, Scotland. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT. E-mail: lwiswll@math.ucl.ac.uk
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Extract

In this note we generalize the following result of Sawyer [5]:

Theorem 1. There is a function ψ on ℝ such that, whenever g is a real-valued Borel measurable function on (a subset of) ℝ. × ℝn-1 with the property that y ↦ g(y, t) is C1 for a.e. t, the set

has measure zero.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory

Information

Type
Research Article
Information
Mathematika , Volume 51 , Issue 1-2 , December 2004 , pp. 155 - 162
Copyright
Copyright © University College London 2004

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References

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