On logarithmic concave measures and functions
On logarithmic concave measures and functions
复制标题
DOI：
--
复制
发表时间：
1973
期刊：
影响因子：
--
通讯作者：
A. Prékopa
中科院分区：
文献类型：
--
作者：
A. Prékopa
本文的目的是为[3]中提供的主要理论提供一个新的证明，并牢记我们理论对数学编程的应用，我们将自己限制在功能和功能和功能上。如果在RN上定义的函数F中有限尺寸的度量是对数凹的+（1 -λ）x2）≥（f（x1））λ（f（x2））1-λ。对于每0 <λ<1，我们都有以下不等式
The purpose of the present paper is to give a new proof for the main theorem proved in [3] and develop further properties of logarithmic concave measures and functions. Having in mind the applications of our theory to mathematical programming, we restrict ourselves to functions and measures in finite dimensional Euclidean spaces. A function f defined on Rn is said to be logarithmic concave if for every pair of vectors x1, x2 ∈ Rn and for every 0 < λ < 1 we have (1.1) f(λx1 + (1 − λ)x2) ≥ (f(x1))λ(f(x2))1−λ. A measure defined on the measurable subsets of Rn is logarithmic concave if for every pair A, B of convex subsets of Rn and for every 0 < λ < 1, we have the following inequality