Open Access
2000/2001 Note on the Outer Measures of Images of Sets
F. S. Cater
Real Anal. Exchange 26(2): 827-830 (2000/2001).


Let $f$ be a real function on ${\mathbb R}$, let $\{I_v\}$ be a family of intervals covering a set $E$ such that $m(E \cap I_v) \ge m\bigl (f(E \cap I_v)\bigr )$ for each $I_v$. We prove that $m\bigl (f(E)\bigr ) \le 2 \cdot m(E)$. No coefficient smaller than $2$ will suffice here in general.


Download Citation

F. S. Cater. "Note on the Outer Measures of Images of Sets." Real Anal. Exchange 26 (2) 827 - 830, 2000/2001.


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

zbMATH: 1009.28006
MathSciNet: MR1844396

Primary: 28A12

Keywords: coverings , Lebesgue outer measure

Rights: Copyright © 2000 Michigan State University Press

Vol.26 • No. 2 • 2000/2001
Back to Top