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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 mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Measurable rigidity of actions on infinite measure homogeneous spaces, II
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by Alex Furman
J. Amer. Math. Soc. 21 (2008), 479-512
Published electronically: December 27, 2007


We consider the problems of measurable isomorphisms and joinings, measurable centralizers and quotients for certain classes of ergodic group actions on infinite measure spaces. Our main focus is on systems of algebraic origin: actions of lattices and other discrete subgroups $\Gamma <G$ on homogeneous spaces $G/H$ where $H$ is a sufficiently rich unimodular subgroup in a semi-simple group $G$. We also consider actions of discrete groups of isometries $\Gamma <\mathrm {Isom}(X)$ of a pinched negative curvature space $X$, acting on the space of horospheres $\mathrm {Hor}(X)$. For such systems we prove that the only measurable isomorphisms, joinings, quotients, etc., are the obvious algebraic (or geometric) ones. This work was inspired by the previous work of Shalom and Steger but uses completely different techniques which lead to more general results.
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Bibliographic Information
  • Alex Furman
  • Affiliation: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607
  • Email:
  • Received by editor(s): March 8, 2006
  • Published electronically: December 27, 2007
  • Additional Notes: The author was supported in part by NSF grant DMS-0094245 and BSF USA-Israel grant 2004345.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 21 (2008), 479-512
  • MSC (2000): Primary 37A17; Secondary 37A35, 22E40, 22F30
  • DOI:
  • MathSciNet review: 2373357