Measurability of equivalence classes and MEC$_p$-property in metric spaces
Järvenpää, Esa ; Järvenpää, Maarit ; Rogovin, Kevin ; Rogovin, Sari ; Shanmugalingam, Nageswari
Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, p. 811-830 / Harvested from Project Euclid
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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.
Publié le : 2007-12-15
Classification:  $\mathrm{MEC}_p$-space,  analytic set,  doubling measure,  weak $p$-Poincaré inequality,  quasi-convexity,  28A05,  28A20,  54E40 
@article{1204128301,
     author = {J\"arvenp\"a\"a, Esa and J\"arvenp\"a\"a, Maarit and Rogovin, Kevin and Rogovin, Sari and Shanmugalingam, Nageswari},
     title = {Measurability of equivalence classes and MEC$\_p$-property
in metric spaces},
     journal = {Rev. Mat. Iberoamericana},
     volume = {23},
     number = {1},
     year = {2007},
     pages = { 811-830},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1204128301}
}

Järvenpää, Esa; Järvenpää, Maarit; Rogovin, Kevin; Rogovin, Sari; Shanmugalingam, Nageswari. Measurability of equivalence classes and MEC$_p$-property
in metric spaces. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp.  811-830. http://gdmltest.u-ga.fr/item/1204128301/