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}
}
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