Marstrand's density theorem in the Heisenberg group

Vasilis Chousionis, Jeremy T. Tyson

Research output: Contribution to journalArticlepeer-review


We prove that if μ is a Radon measure on the Heisenberg group Hn such that the density θ sμ), computed with respect to the Korányi metric dH, exists and is positive and finite on a set of positive μ measure, then s is an integer. The proof relies on an analysis of uniformly distributed measures on Hn, dH. We provide a number of examples of such measures, illustrating both the similarities and the striking differences of this sub-Riemannian setting from its Euclidean counterpart.

Original languageEnglish (US)
Pages (from-to)771-788
Number of pages18
JournalBulletin of the London Mathematical Society
Issue number5
StatePublished - 2014

ASJC Scopus subject areas

  • Mathematics(all)


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