# Convergence of metric two-level measure spaces

@article{Meizis2018ConvergenceOM,
title={Convergence of metric two-level measure spaces},
author={Roland Meizis},
journal={arXiv: Probability},
year={2018}
}
• 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
1

#### Citations

##### Publications citing this paper.
SHOWING 1-2 OF 2 CITATIONS

## Inference with selection, varying population size and evolving population structure: Application of ABC to a forward-backward coalescent process with interactions

• Biology, Mathematics
• 2019
VIEW 1 EXCERPT
CITES BACKGROUND

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 45 REFERENCES

## MARKED METRIC MEASURE SPACES

• Mathematics
• 2011

## Convergence in distribution of random metric measure spaces (Λ-coalescent measure trees)

• Mathematics
• 2009

## Ricci curvature for metric-measure spaces via optimal transport

• Mathematics
• 2004

## Tree-valued resampling dynamics Martingale problems and applications

• Mathematics
• 2008

## Tree-valued Fleming–Viot dynamics with mutation and selection

• Mathematics
• 2012

## A Course in Metric Geometry

• Arcwise Isometries
• 2001