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Israel Journal of Mathematics

, Volume 157, Issue 1, pp 283–308 | Cite as

Degree two ergodic theorem for divergence-free stationary random fields

  • Jérôme Depauw
Article

Abstract

We prove the ergodic theorem for surface integrals of divergence-free stationary random fields of ℝ3. Mean convergence in \( \mathbb{L}^p \) spaces takes place as soon as the field is \( \mathbb{L}^p \)-integrable. The condition of integrability for the pointwise convergence is expressed by a Lorentz norm. This theorem is an ergodic theorem for cocycles of degree 2, analogous to the ergodic theorem for cocycles of degree 1 proved in [1].

Keywords

Ergodic Theorem Weak Sense Cyclic Permutation Lorentz Space Pointwise Convergence 
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Copyright information

© The Hebrew University of Jerusalem 2007

Authors and Affiliations

  • Jérôme Depauw
    • 1
  1. 1.Laboratoire de Mathématiques et Physique Théorique, Faculté des Sciences et TechniquesUniversité de ToursToursFrance

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