Transactions of the American Mathematical Society

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

 

 

Genericity of nontrivial $ H$-superrecurrent $ H$-cocycles


Author: Karma Dajani
Journal: Trans. Amer. Math. Soc. 323 (1991), 111-132
MSC: Primary 28D99; Secondary 34C35, 47A35, 60J15
MathSciNet review: 1018574
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1018574-8
Article copyright: © Copyright 1991 American Mathematical Society