The Topological Support of the z-Measures on the Thoma Simplex

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The Thoma simplex Ω is an infinite-dimensional space, a kind of dual object to the infinite symmetric group. The z-measures are probability measures on Ω depending on three continuous parameters. One of them is the parameter of the Jack symmetric functions, and in the limit as it goes to 0, the z-measures turn into the Poisson–Dirichlet distributions. The definition of the z-measures is somewhat implicit. We show that the topological support of any nondegenerate z-measure is the whole space Ω.

Original languageEnglish
Pages (from-to)308-310
Number of pages3
JournalFunctional Analysis and its Applications
Issue number4
Publication statusPublished - 1 Oct 2018


  • Poisson–Dirichlet distribution
  • symmetric function
  • topological support
  • z-measure


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