Convergence of metric two-level measure spaces

  title={Convergence of metric two-level measure spaces},
  author={Roland Meizis},
  journal={arXiv: Probability},
  • Roland Meizis
  • Published 2018
  • Mathematics
  • arXiv: Probability
  • In this article we extend the notion of metric measure spaces to so-called metric two-level measure spaces (m2m spaces): An m2m space $(X, r, \nu)$ is a Polish metric space $(X, r)$ equipped with a two-level measure $\nu \in \mathcal{M}_f(\mathcal{M}_f(X))$, i.e. a finite measure on the set of finite measures on $X$. We introduce a topology on the set of (equivalence classes of) m2m spaces induced by certain test functions (i.e. the initial topology with respect to these test functions) and… CONTINUE READING
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