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The Abramov-Rokhlin formula

Part of the Lecture Notes in Mathematics book series (LNM,volume 1514)

Abstract

The Abramov-Rokhlin formula states that the entropy of a measure-preserving transformation S equals the sum of the entropy of a factor T of S and the entropy of S relative to T. We prove this formula for non-invertible transformations and apply it to skew-product transformations.

Key words

  • entropy relative to a factor
  • skew-product transformation

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© 1992 Springer-Verlag

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Bogenschütz, T., Crauel, H. (1992). The Abramov-Rokhlin formula. In: Krengel, U., Richter, K., Warstat, V. (eds) Ergodic Theory and Related Topics III. Lecture Notes in Mathematics, vol 1514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0097526

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  • DOI: https://doi.org/10.1007/BFb0097526

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-55444-8

  • Online ISBN: 978-3-540-47076-2

  • eBook Packages: Springer Book Archive