Measurability of equivalence classes and MEC$_p$-property in metric spaces

Esa Järvenpää; Maarit Järvenpää; Kevin Rogovin; Sari Rogovin; Nageswari Shanmugalingam

doi:10.4171/rmi/514

JournalsrmiVol. 23, No. 3pp. 811–830

Measurability of equivalence classes and MEC $_{p}$ -property in metric spaces

Esa Järvenpää
University of Jyväskylä, Finland
Maarit Järvenpää
University of Jyväskylä, Finland
Kevin Rogovin
University of Jyväskylä, Finland
Sari Rogovin
University of Jyväskylä, Finland
Nageswari Shanmugalingam
University of Cincinnati, USA

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Abstract

We prove that a locally compact metric space that supports a doubling measure and a weak $p$ -Poincaré inequality for some $1 \leq p < \infty$ is a $MEC_{p}$ -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.

Cite this article

Esa Järvenpää, Maarit Järvenpää, Kevin Rogovin, Sari Rogovin, Nageswari Shanmugalingam, Measurability of equivalence classes and MEC $_{p}$ -property in metric spaces . Rev. Mat. Iberoam. 23 (2007), no. 3, pp. 811–830

DOI 10.4171/RMI/514