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From Sobolev inequality to doubling

Lyudmila Korobenko, Diego Maldonado, Cristian Rios
2015 Proceedings of the American Mathematical Society  
In various analytical contexts, it is proved that a weak Sobolev inequality implies a doubling property for the underlying measure.
doi:10.1090/s0002-9939-2015-12556-7 fatcat:7eu3eiy7sneexf2o3dz62utjn4