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Paper   IPM / M / 16034
School of Mathematics
  Title:   Metrization of the Gromov-Hausdorff (-Prokhorov) topology for boundedly-compact metric spaces
  Author(s):  Ali Khezeli
  Status:   To Appear
  Journal: Stochastic Processes and Their Applications
  Supported by:  IPM
In this work, it is proved that the set of boundedly-compact pointed metric spaces, equipped with the Gromov- Hausdorff topology, is a Polish space. The same is done for the Gromov-Hausdorff-Prokhorov topology. This extends previous works which consider only length spaces or discrete metric spaces. This is a measure theoretic requirement to study random boundedly-compact pointed (measured) metric spaces, which is the main motivation of this work. In particular, this provides a unified framework for studying random graphs, random discrete spaces and random length spaces. The proofs use a generalization of Strassen�??s theorem, presented here, which is of independent interest.

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