Troyanov, MarcGol'dshtein, Vladimir2007-12-172007-12-172007-12-17200110.1016/S0764-4442(01)02088-2https://infoscience.epfl.ch/handle/20.500.14299/15779WOS:0001718595000101600We prove that the pointwise inequality used by P. Hajlasz in his definition of Sobolev spaces on metric spaces is equivalent to an integral (Poincaré-type) inequality.Sobolev space on metric spacetext::journal::journal article::research article