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Isoperimetric and analytic inequalities for log-concave probability measures. (English) Zbl 0964.60013
It is shown that the probability measures on Euclidean space with logarithmically concave densities have positive isoperimetric constants in the sense of Cheeger and thus always share Poincaré-type inequalities. Then those log-concave measures are described which satisfy inequalities of Gaussian type.

MSC:
60E15 Inequalities; stochastic orderings
46G12 Measures and integration on abstract linear spaces
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