Remarks on the tightness of cocycles

Jon Aaronson; Benjamin Weiss

Colloquium Mathematicae (2000)

  • Volume: 84/85, Issue: 2, page 363-376
  • ISSN: 0010-1354

Abstract

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We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.

How to cite

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Aaronson, Jon, and Weiss, Benjamin. "Remarks on the tightness of cocycles." Colloquium Mathematicae 84/85.2 (2000): 363-376. <http://eudml.org/doc/210819>.

@article{Aaronson2000,
abstract = {We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.},
author = {Aaronson, Jon, Weiss, Benjamin},
journal = {Colloquium Mathematicae},
keywords = {measure preserving transformation; cocycle; tight subset of probability measures},
language = {eng},
number = {2},
pages = {363-376},
title = {Remarks on the tightness of cocycles},
url = {http://eudml.org/doc/210819},
volume = {84/85},
year = {2000},
}

TY - JOUR
AU - Aaronson, Jon
AU - Weiss, Benjamin
TI - Remarks on the tightness of cocycles
JO - Colloquium Mathematicae
PY - 2000
VL - 84/85
IS - 2
SP - 363
EP - 376
AB - We prove a generalised tightness theorem for cocycles over an ergodic probability preserving transformation with values in Polish topological groups. We also show that subsequence tightness of cocycles over a mixing probability preserving transformation implies tightness. An example shows that this latter result may fail for cocycles over a mildly mixing probability preserving transformation.
LA - eng
KW - measure preserving transformation; cocycle; tight subset of probability measures
UR - http://eudml.org/doc/210819
ER -

References

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  13. C. C. Moore and K. Schmidt, Coboundaries and homomorphisms for nonsingular actions and a problem of H. Helson, Proc. London Math. Soc. 40 (1980), 443-475. Zbl0428.28014
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  16. [Sch1] K. Schmidt, Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, MacMillan of India, 1977. Zbl0421.28017
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