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# Volume of spheres in doubling metric measured spaces and in groups of polynomial growth

@inproceedings{Tessera2005VolumeOS, title={Volume of spheres in doubling metric measured spaces and in groups of polynomial growth}, author={Romain Tessera}, year={2005} }

- Published 2005

Let G be a compactly generated locally compact group and let U be a compact generating set. We prove that if G has polynomial growth, then (Un)n∈N is a Følner sequence and we give a polynomial estimate of the rate of decay of μ(U r U) μ(U) . Our proof is based on doubling property. As a matter of fact, the result remains true in a wide class of doubling metric measured spaces including manifolds and graphs. As an application, we obtain a balls averages L-pointwise ergodic theorem for… CONTINUE READING