Existence of mark functions in marked metric measure spaces

  title={Existence of mark functions in marked metric measure spaces},
  author={Sandra Kliem and Wolfgang Lohr},
  journal={Electronic Journal of Probability},
We give criteria on the existence of a so-called mark function in the context of marked metric measure spaces (mmm-spaces). If an mmm-space admits a mark function, we call it functionally-marked metric measure space (fmm-space). This is not a closed property in the usual marked Gromov-weak topology, and thus we put particular emphasis on the question under which conditions it carries over to a limit. We obtain criteria for deterministic mmm-spaces as well as random mmm-spaces and mmm-space… 
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