Open Access
2000/2001 Graphs of Functions, Regular Sets and S-Straight Sets
R. Delaware, L. Eifler
Real Anal. Exchange 26(2): 893-900 (2000/2001).


A subset $E$ of $\Bbb{R}^p$ is s-straight if $E$ has finite Hausdorff s-dimensional outer measure which equals its Method I s-outer measure. The graph of a continuously differentiable function is shown to be the countable union of closed 1-straight sets together with a set of Hausdorff 1-measure zero. This result is extended to the graphs of absolutely continuous functions and to regular sets.


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R. Delaware. L. Eifler. "Graphs of Functions, Regular Sets and S-Straight Sets." Real Anal. Exchange 26 (2) 893 - 900, 2000/2001.


Published: 2000/2001
First available in Project Euclid: 27 June 2008

zbMATH: 1010.28006
MathSciNet: MR1844402

Primary: 28A05 , 28A78

Keywords: Hausdorff measure , regular sets , s-straight sets

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 2 • 2000/2001
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