A Universality Property of Sobolev Spaces in Metric Measure Spaces

  • Nageswari Shanmugalingam
Part of the International Mathematical Series book series (IMAT, volume 8)


Current research on analysis in metric measure spaces has used alternative notions of Sobolev functions on metric measure spaces. We show that, under some mild geometric assumptions on the metric measure space, all these notions give the same class of functions.


Sobolev Space Measure Space Lipschitz Function Dirichlet Form Sobolev Function 
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© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Nageswari Shanmugalingam
    • 1
  1. 1.University of CincinnatiCincinnatiUSA

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