We study some problems on exponential integrability, concentration of measure, and transportation cost related to logarithmic Sobolev inequalities. On the real line, we then give a characterization of those probability measures which satisfy these inequalities
Bibliographical noteFunding Information:
* Research supported in part by Alexander von Humboldt Foundation.
- Concentration of measure
- Exponential integrability
- Logarithmic Sobolev inequalities
- Transportation inequalities