### Abstract

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

Original language | English |
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Pages (from-to) | 4493-4501 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 145 |

Issue number | 10 |

DOIs | |

Publication status | Published - 2017 |

### Keywords

- Metric measure space
- Observable distance
- Talagrand’s inequality

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Ozawa, R., & Suzuki, N. (2017). Stability of Talagrand’s inequality under concentration topology.

*Proceedings of the American Mathematical Society*,*145*(10), 4493-4501. https://doi.org/10.1090/proc/13580