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PreprintCC BY 4.0arXiv

Pyramidal Compactification of Asymmetric Metric Measure Spaces via Adjoint Transport

  • Shigeaki Yokota
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Abstract

A quasi-metric measure space (qm-space) is a set with a directed distance whose symmetrization is a complete separable metric, together with a Borel probability measure of full support. Motivated by the problem of determining the pyramid limits of beta measures on forward Funk balls, we construct a compact metric space of pyramids of qm-spaces. The associated-pyramid map from the concentration-distance space of qm-spaces into this compact space is a $1$-Lipschitz topological embedding with dense image. As a secondary result, we prove that the box-distance space of qm-spaces is complete and separable.

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Cite

BibTeXRIS
BibTeX
@misc{yokota2026pyramidal,
  title = {{Pyramidal Compactification of Asymmetric Metric Measure Spaces via Adjoint Transport}},
  author = {Shigeaki Yokota},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.01145},
  eprint = {2608.01145},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.01145},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Pyramidal Compactification of Asymmetric Metric Measure Spaces via Adjoint Transport
AU  - Shigeaki Yokota
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2608.01145
UR  - https://arxiv.org/abs/2608.01145
AB  - A quasi-metric measure space (qm-space) is a set with a directed distance whose symmetrization is a complete separable metric, together with a Borel probability measure of full support. Motivated by the problem of determining the pyramid limits of beta measures on forward Funk balls, we construct a compact metric space of pyramids of qm-spaces. The associated-pyramid map from the concentration-distance space of qm-spaces into this compact space is a $1$-Lipschitz topological embedding with dense image. As a secondary result, we prove that the box-distance space of qm-spaces is complete and separable.
ER  -