---
_id: '15252'
abstract:
- lang: eng
  text: A measurable map between measure spaces is shown to have bounded compression
    if and only if its image via the measure-algebra functor is Lipschitz-continuous
    w.r.t. the measure-algebra distances. This provides a natural interpretation of
    maps of bounded compression/deformation by means of the measure-algebra functor
    and corrobo-rates the assertion that maps of bounded deformation are a natural
    class of morphisms for the category of complete and separable metric measure spaces.
acknowledgement: "The author gratefully acknowledges funding of his current position
  by the Austrian Science\r\nFund (FWF), grant ESPRIT208. He is grateful to Enrico
  Pasqualetto for pointing out some\r\nreferences on maps of bounded compression."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lorenzo
  full_name: Dello Schiavo, Lorenzo
  id: ECEBF480-9E4F-11EA-B557-B0823DDC885E
  last_name: Dello Schiavo
  orcid: 0000-0002-9881-6870
citation:
  ama: Dello Schiavo L. A characterization of maps of bounded compression. <i>Mathematical
    Communications</i>. 2024;29(1):137-142.
  apa: Dello Schiavo, L. (2024). A characterization of maps of bounded compression.
    <i>Mathematical Communications</i>. Udruga Matematicara Osijek.
  chicago: Dello Schiavo, Lorenzo. “A Characterization of Maps of Bounded Compression.”
    <i>Mathematical Communications</i>. Udruga Matematicara Osijek, 2024.
  ieee: L. Dello Schiavo, “A characterization of maps of bounded compression,” <i>Mathematical
    Communications</i>, vol. 29, no. 1. Udruga Matematicara Osijek, pp. 137–142, 2024.
  ista: Dello Schiavo L. 2024. A characterization of maps of bounded compression.
    Mathematical Communications. 29(1), 137–142.
  mla: Dello Schiavo, Lorenzo. “A Characterization of Maps of Bounded Compression.”
    <i>Mathematical Communications</i>, vol. 29, no. 1, Udruga Matematicara Osijek,
    2024, pp. 137–42.
  short: L. Dello Schiavo, Mathematical Communications 29 (2024) 137–142.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-03-31T22:01:12Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2026-10-02T12:15:11Z
day: '01'
department:
- _id: JaMa
external_id:
  arxiv:
  - '2304.11348'
intvolume: '        29'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2304.11348
month: '01'
oa: 1
oa_version: Preprint
page: 137-142
project:
- _id: 34dbf174-11ca-11ed-8bc3-afe9d43d4b9c
  grant_number: E208
  name: Configuration Spaces over Non-Smooth Spaces
publication: Mathematical Communications
publication_identifier:
  eissn:
  - 1848-8013
  issn:
  - 1331-0623
publication_status: published
publisher: Udruga Matematicara Osijek
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: A characterization of maps of bounded compression
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 29
year: '2024'
...