{"publication_status":"published","date_published":"2019-01-30T00:00:00Z","conference":{"start_date":"2019-01-28","name":"Research on isometries as preserver problems and related topics","end_date":"2019-01-30","location":"Kyoto, Japan"},"citation":{"mla":"Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” <i>Kyoto RIMS Kôkyûroku</i>, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,” in <i>Kyoto RIMS Kôkyûroku</i>, Kyoto, Japan, 2019, vol. 2125, pp. 34–41.","ama":"Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In: <i>Kyoto RIMS Kôkyûroku</i>. Vol 2125. Research Institute for Mathematical Sciences, Kyoto University; 2019:34-41.","apa":"Geher, G. P., Titkos, T., &#38; Virosztek, D. (2019). Dirac masses and isometric rigidity. In <i>Kyoto RIMS Kôkyûroku</i> (Vol. 2125, pp. 34–41). Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University.","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.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and Isometric Rigidity.” In <i>Kyoto RIMS Kôkyûroku</i>, 2125:34–41. Research Institute for Mathematical Sciences, Kyoto University, 2019.","short":"G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41."},"department":[{"_id":"LaEr"}],"language":[{"iso":"eng"}],"_id":"7035","main_file_link":[{"url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html","open_access":"1"}],"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."}],"type":"conference","page":"34-41","author":[{"first_name":"Gyorgy Pal","last_name":"Geher","full_name":"Geher, Gyorgy Pal"},{"full_name":"Titkos, Tamas","last_name":"Titkos","first_name":"Tamas"},{"orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","last_name":"Virosztek"}],"day":"30","publication":"Kyoto RIMS Kôkyûroku","article_processing_charge":"No","month":"01","date_updated":"2021-01-12T08:11:33Z","title":"Dirac masses and isometric rigidity","quality_controlled":"1","status":"public","oa":1,"intvolume":"      2125","oa_version":"Submitted Version","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_created":"2019-11-18T15:39:53Z","volume":2125,"publisher":"Research Institute for Mathematical Sciences, Kyoto University","year":"2019"}