Genericity of nontrivial 𝐻-superrecurrent 𝐻-cocycles

Dajani, Karma

doi:10.1090/S0002-9947-1991-1018574-8

Genericity of nontrivial $H$-superrecurrent $H$-cocycles
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by Karma Dajani

Trans. Amer. Math. Soc. 323 (1991), 111-132

DOI: https://doi.org/10.1090/S0002-9947-1991-1018574-8

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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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