On extremal and perfect σ-algebras for flows

B. Kamiński; Z. Kowalski

Studia Mathematica (1998)

  • Volume: 129, Issue: 2, page 179-183
  • ISSN: 0039-3223

Abstract

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It is shown that there exists a flow on a Lebesgue space with finite entropy and an extremal σ-algebra of it which is not perfect.

How to cite

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Kamiński, B., and Kowalski, Z.. "On extremal and perfect σ-algebras for flows." Studia Mathematica 129.2 (1998): 179-183. <http://eudml.org/doc/216497>.

@article{Kamiński1998,
abstract = {It is shown that there exists a flow on a Lebesgue space with finite entropy and an extremal σ-algebra of it which is not perfect.},
author = {Kamiński, B., Kowalski, Z.},
journal = {Studia Mathematica},
keywords = {special flow; entropy; extremal -algebra; measurable flow action; Pinsker -algebra},
language = {eng},
number = {2},
pages = {179-183},
title = {On extremal and perfect σ-algebras for flows},
url = {http://eudml.org/doc/216497},
volume = {129},
year = {1998},
}

TY - JOUR
AU - Kamiński, B.
AU - Kowalski, Z.
TI - On extremal and perfect σ-algebras for flows
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 2
SP - 179
EP - 183
AB - It is shown that there exists a flow on a Lebesgue space with finite entropy and an extremal σ-algebra of it which is not perfect.
LA - eng
KW - special flow; entropy; extremal -algebra; measurable flow action; Pinsker -algebra
UR - http://eudml.org/doc/216497
ER -

References

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  1. [1] F. Blanchard, Partitions extrêmales des flots d'entropie infinie, Z. Wahrsch. Verw. Gebiete 36 (1976), 129-136. Zbl0319.28012
  2. [2] F. Blanchard, K-flots et théorème de renouvellement, ibid., 345-358. Zbl0328.60036
  3. [3] M. Binkowska and B. Kamiński, Entropy increase for ℤ d -actions on a Lebesgue space, Israel J. Math. 88 (1994), 307-318. Zbl0826.28008
  4. [4] S. Goldstein and O. Penrose, A non-equilibrium entropy for dynamical systems, J. Statist. Phys. 24 (1981), 325-343. Zbl0516.70021
  5. [5] B. M. Gurevich, Some existence conditions for K-decompositions for special flows, Trans. Moscow Math. Soc. 17 (1967), 99-126. Zbl0207.48502
  6. [6] B. M. Gurevich, Perfect partitions for ergodic flows, Funktsional. Anal. i Prilozhen. 11 (3) (1977), 20-23 (in Russian). 
  7. [7] B. Kamiński, The theory of invariant partitions for ℤ d -actions, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 349-362. Zbl0479.28016
  8. [8] B. Kamiński, Z. S. Kowalski and P. Liardet, On extremal and perfect σ-algebras for ℤ d -actions, Studia Math. 124 (1997), 173-178. Zbl0882.28015
  9. [9] V. A. Rokhlin, Lectures on the entropy theory of measure-preserving transformations, Uspekhi Mat. Nauk 22 (5) (1967), 3-56 (in Russian). 
  10. [10] T. Shimano, An invariant of systems in the ergodic theory, Tôhoku Math. J. 30 (1978), 337-350. Zbl0394.28009
  11. [11] T. Shimano, Multiplicity of helices of a special flow, ibid. 31 (1979), 49-55. Zbl0412.28011
  12. [12] T. Shimano, Multiplicity of helices for a regularly increasing sequence of σ-fields, ibid. 36 (1984), 141-148. Zbl0551.28021
  13. [13] T. Shimano, On helices for Kolmogorov system with two indices, Math. J. Toyama Univ. 14 (1991), 213-226. Zbl0768.60031

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