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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Structure of measures in Lipschitz differentiability spaces
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by David Bate PDF
J. Amer. Math. Soc. 28 (2015), 421-482 Request permission


We prove the equivalence of two seemingly very different ways of generalising Rademacher’s theorem to metric measure spaces. One such generalisation is based upon the notion of forming partial derivatives along a very rich structure of Lipschitz curves in a way analogous to the differentiability theory of Euclidean spaces. This approach to differentiability in this generality appears here for the first time and by examining this structure further, we naturally arrive to several descriptions of Lipschitz differentiability spaces.
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Additional Information
  • David Bate
  • Affiliation: Department of Mathematics, Mathematics Institute, Zeeman Building, University of Warwick, Coventry, CV4 7AL, UK
  • Address at time of publication: Department of Mathematics, University of Chicago, 5734 S. University Avenue, Room 208C, Chicago, Illinois 60637
  • Email:,
  • Received by editor(s): August 10, 2012
  • Received by editor(s) in revised form: February 6, 2014
  • Published electronically: June 4, 2014
  • Additional Notes: I would like to thank David Preiss for his dedicated reading of this manuscript and for our insightful conversations throughout my time as his student. I would also like to thank Guy C. David (UCLA) for spotting a technical error in the first version of Section 6. This work was supported by the EPSRC
  • © Copyright 2014 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 28 (2015), 421-482
  • MSC (2010): Primary 30L99; Secondary 49J52, 53C23
  • DOI:
  • MathSciNet review: 3300699