---
_id: '7035'
abstract:
- lang: eng
text: 'The aim of this short note is to expound one particular issue that was discussed
during the talk [10] given at the symposium ”Researches on isometries as preserver
problems and related topics” at Kyoto RIMS. That is, the role of Dirac masses
by describing the isometry group of various metric spaces of probability measures. This article is of survey character, and it does not contain any essentially new
results.From an isometric point of view, in some cases, metric spaces of measures
are similar to C(K)-type function spaces. Similarity means here that their isometries are driven by some nice transformations
of the underlying space. Of course, it depends on the particular choice of the metric how nice these
transformations should be. Sometimes, as we will see, being a homeomorphism is
enough to generate an isometry. But sometimes we need more: the transformation
must preserve the underlying distance as well. Statements claiming that isometries
in questions are necessarily induced by homeomorphisms are called Banach-Stone-type
results, while results asserting that the underlying transformation is necessarily
an isometry are termed as isometric rigidity results.As Dirac masses can be considered as building bricks of the set of all Borel measures, a natural
question arises:Is it enough to understand how an isometry acts on the set of
Dirac masses? Does this action extend uniquely to all measures?In what follows,
we will thoroughly investigate this question.'
article_processing_charge: No
author:
- first_name: Gyorgy Pal
full_name: Geher, Gyorgy Pal
last_name: Geher
- first_name: Tamas
full_name: Titkos, Tamas
last_name: Titkos
- first_name: Daniel
full_name: Virosztek, Daniel
id: 48DB45DA-F248-11E8-B48F-1D18A9856A87
last_name: Virosztek
citation:
ama: 'Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In:
*Kyoto RIMS Kôkyûroku*. Vol 2125. Research Institute for Mathematical Sciences,
Kyoto University; 2019:34-41.'
apa: 'Geher, G. P., Titkos, T., & Virosztek, D. (2019). Dirac masses and isometric
rigidity. In *Kyoto RIMS Kôkyûroku* (Vol. 2125, pp. 34–41). Kyoto, Japan:
Research Institute for Mathematical Sciences, Kyoto University.'
chicago: Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and
Isometric Rigidity.” In *Kyoto RIMS Kôkyûroku*, 2125:34–41. Research Institute
for Mathematical Sciences, Kyoto University, 2019.
ieee: G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,”
in *Kyoto RIMS Kôkyûroku*, Kyoto, Japan, 2019, vol. 2125, pp. 34–41.
ista: Geher GP, Titkos T, Virosztek D. 2019. Dirac masses and isometric rigidity.
Kyoto RIMS Kôkyûroku. Research on isometries as preserver problems and related
topics vol. 2125. 34–41.
mla: Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” *Kyoto RIMS
Kôkyûroku*, vol. 2125, Research Institute for Mathematical Sciences, Kyoto
University, 2019, pp. 34–41.
short: G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research
Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.
conference:
end_date: 2019-01-30
location: Kyoto, Japan
name: Research on isometries as preserver problems and related topics
start_date: 2019-01-28
date_created: 2019-11-18T15:39:53Z
date_published: 2019-01-30T00:00:00Z
date_updated: 2019-12-02T13:33:50Z
day: '30'
department:
- _id: LaEr
intvolume: ' 2125'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html
month: '01'
oa: 1
oa_version: Submitted Version
page: 34-41
publication: Kyoto RIMS Kôkyûroku
publication_status: published
publisher: Research Institute for Mathematical Sciences, Kyoto University
quality_controlled: '1'
status: public
title: Dirac masses and isometric rigidity
type: conference
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 2125
year: '2019'
...