Aperiodic transformations

G. Helmberg; F.H. Simons

doi:10.1007/BF00537023

Aperiodic transformations

G. Helmberg
, F.H. Simons

Mathematics and Computer Science

Research output: Contribution to journal › Article › Academic › peer-review

7 Citations (Scopus)

Abstract

The concepts of periodicity and aperiodicity are extended so as to apply to any measurable non-singular transformation T in s-finite measure space (X,v,M). Aperiodicity of T may then be characterized by the existence of sweep-out sets with certain properties and turns out to be closely related to the existence of a strong generator for the s-algebra v. This extends recent results of Parry and Rokhlin obtained for Lebesgue spaces.

Original language	English
Pages (from-to)	180-190
Number of pages	11
Journal	Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete
Volume	13
Issue number	2
DOIs	https://doi.org/10.1007/BF00537023
Publication status	Published - 1969

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title = "Aperiodic transformations",

abstract = "The concepts of periodicity and aperiodicity are extended so as to apply to any measurable non-singular transformation T in s-finite measure space (X,v,M). Aperiodicity of T may then be characterized by the existence of sweep-out sets with certain properties and turns out to be closely related to the existence of a strong generator for the s-algebra v. This extends recent results of Parry and Rokhlin obtained for Lebesgue spaces.",

author = "G. Helmberg and F.H. Simons",

year = "1969",

doi = "10.1007/BF00537023",

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TY - JOUR

T1 - Aperiodic transformations

AU - Helmberg, G.

AU - Simons, F.H.

PY - 1969

Y1 - 1969

N2 - The concepts of periodicity and aperiodicity are extended so as to apply to any measurable non-singular transformation T in s-finite measure space (X,v,M). Aperiodicity of T may then be characterized by the existence of sweep-out sets with certain properties and turns out to be closely related to the existence of a strong generator for the s-algebra v. This extends recent results of Parry and Rokhlin obtained for Lebesgue spaces.

AB - The concepts of periodicity and aperiodicity are extended so as to apply to any measurable non-singular transformation T in s-finite measure space (X,v,M). Aperiodicity of T may then be characterized by the existence of sweep-out sets with certain properties and turns out to be closely related to the existence of a strong generator for the s-algebra v. This extends recent results of Parry and Rokhlin obtained for Lebesgue spaces.

U2 - 10.1007/BF00537023

DO - 10.1007/BF00537023

M3 - Article

SN - 0044-3719

VL - 13

SP - 180

EP - 190

JO - Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete

JF - Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete

IS - 2

ER -

Aperiodic transformations

Abstract

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