JournalsrmiVol. 23, No. 3pp. 811–830

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

We prove that a locally compact metric space that supports a doubling measure and a weak pp-Poincaré inequality for some 1p<1\le p < \infty is a MECp\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 pp-integrable upper gradient is locally pp-integrable.

Cite this article

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

DOI 10.4171/RMI/514