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Pointwise Ergodic Theorems

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Ergodic Theorems for Group Actions

Part of the book series: Mathematics and Its Applications ((MAIA,volume 78))

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Abstract

We denote by \({\tilde F_B} = {\tilde F_B}(\Omega ,F,m)\) the space of all measurable B-valued functions with the seminorm

$$|f|{P_b} = \mathop {\inf }\limits_{\alpha \geqslant 0} arctam[\alpha + m(\{ \omega :|f(\omega )|\} )];$$

convergence in \({\tilde F_R}\) is the same as convergence in m.

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Authors and Affiliations

  1. Department of Statistics, Penn State University, University Park, USA

    Arkady Tempelman

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  1. Arkady Tempelman
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© 1992 Springer Science+Business Media Dordrecht

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Tempelman, A. (1992). Pointwise Ergodic Theorems. In: Ergodic Theorems for Group Actions. Mathematics and Its Applications, vol 78. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1460-0_7

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  • DOI: https://doi.org/10.1007/978-94-017-1460-0_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4155-5

  • Online ISBN: 978-94-017-1460-0

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