Open Access
Decembar, 2007 Measurability of equivalence classes and MEC$_p$-property in metric spaces
Esa Järvenpää, Maarit Järvenpää, Kevin Rogovin, Sari Rogovin, Nageswari Shanmugalingam
Rev. Mat. Iberoamericana 23(3): 811-830 (Decembar, 2007).


We prove that a locally compact metric space that supports a doubling measure and a weak $p$-Poincaré inequality for some $1\le p < \infty$ is a $\mathrm{MEC}_p$-space. The methods developed for this purpose include measurability considerations and lead to interesting consequences. For example, we verify that each extended real valued function having a $p$-integrable upper gradient is locally $p$-integrable.


Download Citation

Esa Järvenpää. Maarit Järvenpää. Kevin Rogovin. Sari Rogovin. Nageswari Shanmugalingam. "Measurability of equivalence classes and MEC$_p$-property in metric spaces." Rev. Mat. Iberoamericana 23 (3) 811 - 830, Decembar, 2007.


Published: Decembar, 2007
First available in Project Euclid: 27 February 2008

zbMATH: 1146.28001
MathSciNet: MR2414493

Primary: 28A05 , 28A20 , 54E40

Keywords: $\mathrm{MEC}_p$-space , analytic set , doubling measure , quasi-convexity , weak $p$-Poincaré inequality

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.23 • No. 3 • Decembar, 2007
Back to Top