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              <p>Ces aro convergence of spherical averages is proven for measure-preserving actions of Markov semigroups and groups. Convergence in the mean is established for functions in L p , 1 ≤ p &lt; ∞, and pointwise convergence for functions in L ∞. In particular, for measure-preserving actions of word hyperbolic groups (in the sense of Gromov) we obtain Ces aro convergence of spherical averages with respect to any symmetric set of generators.</p>
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