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FAILURE OF THE
$L^{1}$ POINTWISE AND MAXIMAL ERGODIC THEOREMS FOR THE FREE GROUP
Published online by Cambridge University Press: 01 December 2015
Abstract
Let $F_{2}$ denote the free group on two generators
$a$ and
$b$. For any measure-preserving system
$(X,{\mathcal{X}},{\it\mu},(T_{g})_{g\in F_{2}})$ on a finite measure space
$X=(X,{\mathcal{X}},{\it\mu})$, any
$f\in L^{1}(X)$, and any
$n\geqslant 1$, define the averaging operators















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- Research Article
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- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- © The Author 2015
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