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2000 | 84/85 | 2 | 363-376
Tytuł artykułu

Remarks on the tightness of cocycles

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
Numer
2
Strony
363-376
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-08-13
poprawiono
1999-12-04
Twórcy
autor
  • School of Mathematical Sciences, Tel Aviv University, 69978 Tel Aviv, Israel
  • Mathematical Institute, Hebrew University, Jerusalem, Israel
Bibliografia
  • [A] J. Aaronson, An Introduction to Infinite Ergodic Theory, Math. Surveys Monogr. 50, Amer. Math. Soc., Providence, RI, 1997.
  • [Br1] R. C. Bradley, On a theorem of K. Schmidt, Statist. Probab. Lett. 23 (1995), 9-12.
  • [Br2] R. C. Bradley, A 'coboundary' theorem for sums of random variables taking values in a Banach space, Pacific J. Math. 178 (1997), 201-224.
  • [Br3] R. C. Bradley, A 'multiplicative coboundary' theorem for some sequences of random matrices, J. Theoret. Probab. 9 (1996), 659-678.
  • [Br4] R. C. Bradley, On the dissipation of the partial sums of a stationary strongly mixing sequence, Stochastic Process. Appl. 54 (1994), 281-290.
  • [Cha] R. V. Chacon, Weakly mixing transformations which are not strongly mixing, Proc. Amer. Math. Soc. 22 (1969), 559-562.
  • [Co] J.-P. Conze, Transformations cylindriques et mesures finies invariantes, Ann. Sci. Univ. Clermont Math. 17 (1979), 25-31.
  • [Fr] N. Friedman, Introduction to Ergodic Theory, van Nostrand, New York, 1970.
  • [F-K] N. Friedman and J. King, Rank one lightly mixing, Israel J. Math. 73 (1991), 281-288.
  • H. Keynes and D. Newton, The structure of ergodic measures for compact group extensions, Israel J. Math. 18 (1974), 363-389.
  • [Lem] M. Lemańczyk, Ergodic compact Abelian group extensions, habilitation thesis, Nicholas Copernicus Univ., Toruń, 1990.
  • [Leo] V. P. Leonov, On the dispersion of time averages of a stationary random process, Theory Probab. Appl. 6 (1961), 93-101.
  • 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.
  • [Par] K. R. Parthasarathy, Introduction to Probability and Measure, Springer, New York, 1978.
  • [Rev] P. Revesz, On a problem of Steinhaus, Acta Math. Acad. Sci. Hungar. 16 (1965), 311-318.
  • [Sch1] K. Schmidt, Cocycles of Ergodic Transformation Groups, Lecture Notes in Math. 1, MacMillan of India, 1977.
  • [Sch2] K. Schmidt, Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions, Ergodic Theory Dynam. Systems 1 (1981), 223-236.
  • [Weil] A. Weil, L'intégration dans les groupes topologiques et ses applications, Actualités Sci. Indust. 869, Hermann, Paris, 1940.
  • [Zim] R. J. Zimmer, On the cohomology of ergodic group actions, Israel J. Math. 35 (1980), 289-300.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-cmv84i2p363bwm
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