---
_id: '284'
abstract:
- lang: eng
  text: "Borel probability measures living on metric spaces are fundamental\r\nmathematical
    objects. There are several meaningful distance functions that make the collection
    of the probability measures living on a certain space a metric space. We are interested
    in the description of the structure of the isometries of such metric spaces. We
    overview some of the recent results of the topic and we also provide some new
    ones concerning the Wasserstein distance. More specifically, we consider the space
    of all Borel probability measures on the unit sphere of a Euclidean space endowed
    with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the
    action of a Wasserstein isometry on the set of Dirac measures is induced by an
    isometry of the underlying unit sphere."
acknowledgement: The author was supported by the ISTFELLOW program of the Institute
  of Science and Technol- ogy Austria (project code IC1027FELL01) and partially supported
  by the Hungarian National Research, Development and Innovation Office, NKFIH (grant
  no. K124152).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Daniel
  full_name: Virosztek, Daniel
  id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
  last_name: Virosztek
  orcid: 0000-0003-1109-5511
citation:
  ama: Virosztek D. Maps on probability measures preserving certain distances - a
    survey and some new results. <i>Acta Scientiarum Mathematicarum</i>. 2018;84(1-2):65-80.
    doi:<a href="https://doi.org/10.14232/actasm-018-753-y">10.14232/actasm-018-753-y</a>
  apa: Virosztek, D. (2018). Maps on probability measures preserving certain distances
    - a survey and some new results. <i>Acta Scientiarum Mathematicarum</i>. Springer
    Nature. <a href="https://doi.org/10.14232/actasm-018-753-y">https://doi.org/10.14232/actasm-018-753-y</a>
  chicago: Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances
    - a Survey and Some New Results.” <i>Acta Scientiarum Mathematicarum</i>. Springer
    Nature, 2018. <a href="https://doi.org/10.14232/actasm-018-753-y">https://doi.org/10.14232/actasm-018-753-y</a>.
  ieee: D. Virosztek, “Maps on probability measures preserving certain distances -
    a survey and some new results,” <i>Acta Scientiarum Mathematicarum</i>, vol. 84,
    no. 1–2. Springer Nature, pp. 65–80, 2018.
  ista: Virosztek D. 2018. Maps on probability measures preserving certain distances
    - a survey and some new results. Acta Scientiarum Mathematicarum. 84(1–2), 65–80.
  mla: Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances
    - a Survey and Some New Results.” <i>Acta Scientiarum Mathematicarum</i>, vol.
    84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:<a href="https://doi.org/10.14232/actasm-018-753-y">10.14232/actasm-018-753-y</a>.
  short: D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80.
date_created: 2018-12-11T11:45:36Z
date_published: 2018-06-04T00:00:00Z
date_updated: 2023-10-16T10:29:22Z
day: '04'
department:
- _id: LaEr
doi: 10.14232/actasm-018-753-y
ec_funded: 1
external_id:
  arxiv:
  - '1802.03305'
intvolume: '        84'
issue: 1-2
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1802.03305
month: '06'
oa: 1
oa_version: Preprint
page: 65 - 80
project:
- _id: 25681D80-B435-11E9-9278-68D0E5697425
  call_identifier: FP7
  grant_number: '291734'
  name: International IST Postdoc Fellowship Programme
publication: Acta Scientiarum Mathematicarum
publication_identifier:
  eissn:
  - 2064-8316
  issn:
  - 0001-6969
publication_status: published
publisher: Springer Nature
publist_id: '7615'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maps on probability measures preserving certain distances - a survey and some
  new results
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 84
year: '2018'
...