## Abstract

Given measure preserving transformations T_{ 1}, T_{ 2},..., T_{ s} of a probability space (X, B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form {Mathematical expression} where f_{ 1}, f_{ 2},..., f_{ s} e{open}L^{ ∞}(X, B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) in L^{ 2}-norm is ∫_{ x} f_{ 1} dμ·∫_{ x} f_{ 2} dμ...∫_{ x} f_{ s} dμ for any f_{ 1}, f_{ 2}..., f_{ s} e{open}L^{ ∞}(X, B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups.

Original language | English |
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Pages (from-to) | 123-142 |

Number of pages | 20 |

Journal | Journal d'Analyse Mathematique |

Volume | 50 |

Issue number | 1 |

DOIs | |

State | Published - 1 Dec 1988 |

## ASJC Scopus subject areas

- Analysis
- General Mathematics