Gromov’s compactness theorem for metric spaces, a compactness theorem for the space of compact metric spaces equipped with the Gromov-Hausdorff distance, is a landmark theorem with many applications. We give a generalisation of this result - more precisely, we prove a compactness theorem for the space of distance measure spaces equipped with the generalised Gromov-Hausdorff-Levi-Prokhorov distance. A distance measure space is a triple (X, d, μ), where (X, d) forms a distance space (a generalisation of a metric space where, we allow the distance between two points to be infinity) and μ is a finite Borel measure.

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