Measurability of equivalence classes and MEC-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

Abstract

We prove that a locally compact metric space that supports a doubling measure and a weak -Poincaré inequality for some is a -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 -integrable upper gradient is locally -integrable.

Cite this article

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

DOI 10.4171/RMI/514