@article{fa9a41af50464bc8b33ea9039df4654f,

title = "Stability of Talagrand{\textquoteright}s inequality under concentration topology",

abstract = "In this paper, we study the compatibility between Talagrand{\textquoteright}s inequality and the concentration topology; i.e., if a sequence of mm-spaces satisfying Talagrand{\textquoteright}s inequality converges with respect to the observable distance, then the limit space satisfies Talagrand{\textquoteright}s inequality.",

keywords = "Metric measure space, Observable distance, Talagrand{\textquoteright}s inequality",

author = "Ryunosuke Ozawa and Norihiko Suzuki",

note = "Funding Information: Received by the editors July 18, 2016 and, in revised form, November 1, 2016. 2010 Mathematics Subject Classification. Primary 53C23; Secondary 60E15. Key words and phrases. Metric measure space, observable distance, Talagrand{\textquoteright}s inequality. The first author was supported by JSPS KAKENHI Grant No. 24224002 and postdoctoral program at Max Planck Institute for Mathematics. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

year = "2017",

doi = "10.1090/proc/13580",

language = "English",

volume = "145",

pages = "4493--4501",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "10",

}