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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Genericity of nontrivial $H$-superrecurrent $H$-cocycles
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by Karma Dajani PDF
Trans. Amer. Math. Soc. 323 (1991), 111-132 Request permission

Abstract:

We prove that most ${\text {H}}$-cocycles for a nonsingular ergodic transformation of type ${\text {II}}{{\text {I}}_\lambda }$, $0 < \lambda < 1$, are ${\text {H}}$-superrecurrent. This is done by showing that the set of nontrivial ${\text {H}}$-superrecurrent ${\text {H}}$-cocycles form a dense ${G_\delta }$ set with respect to the topology of convergence in measure.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 323 (1991), 111-132
  • MSC: Primary 28D99; Secondary 34C35, 47A35, 60J15
  • DOI: https://doi.org/10.1090/S0002-9947-1991-1018574-8
  • MathSciNet review: 1018574