# Subsets of Virtually Nilpotent Groups with the SBM Property

@inproceedings{Burkhart2022SubsetsOV, title={Subsets of Virtually Nilpotent Groups with the SBM Property}, author={Ryan Burkhart and Isaac Goldbring}, year={2022} }

. We extend Leth’s notion of subsets of the integers satisfying the Standard interval measure (SIM) property to the class of virtually nilpotent groups and name the corresponding property the Standard ball measure (SBM) property. In order to do this, we deﬁne a natural measure on closed balls in asymptotic cones associated to such groups and show that this measure satisﬁes the Lebesgue density theorem. We then prove analogs of various properties known to hold for SIM sets in this broader…

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