Pogorzelski, FelixRichard, ChristophStrungaru, Nicolae2024-01-052024-01-052022Pogorzelski, F., Richard, C., & Strungaru, N. (2022). Leptin Densities in Amenable Groups. Journal of Fourier Analysis and Applications, 28, 85. https://doi.org/10.1007/s00041-022-09978-8https://hdl.handle.net/20.500.14078/3326Consider a positive Borel measure on a locally compact group. We define a notion of uniform density for such a measure, which is based on a group invariant introduced by Leptin in 1966. We then restrict to unimodular amenable groups and to translation bounded measures. In that case our density notion coincides with the well-known Beurling density from Fourier analysis, also known as Banach density from dynamical systems theory. We use Leptin densities for a geometric proof of the model set density formula, which expresses the density of a uniform regular model set in terms of the volume of its window, and for a proof of uniform mean almost periodicity of such model sets.enAttribution (CC BY)amenabilityFølner netBeurling densityBanach densitymodel setalmost periodicityArticlehttps://doi.org/10.1007/s00041-022-09978-8