---
res:
bibo_abstract:
- '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.@eng'
bibo_authorlist:
- foaf_Person:
foaf_givenName: Gyorgy Pal
foaf_name: Geher, Gyorgy Pal
foaf_surname: Geher
- foaf_Person:
foaf_givenName: Tamas
foaf_name: Titkos, Tamas
foaf_surname: Titkos
- foaf_Person:
foaf_givenName: Daniel
foaf_name: Virosztek, Daniel
foaf_surname: Virosztek
foaf_workInfoHomepage: http://www.librecat.org/personId=48DB45DA-F248-11E8-B48F-1D18A9856A87
bibo_volume: 2125
dct_date: 2019^xs_gYear
dct_language: eng
dct_publisher: Research Institute for Mathematical Sciences, Kyoto University@
dct_title: Dirac masses and isometric rigidity@
...