Triangular transformations of measures
Triangular transformations of measures
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DOI：
10.1070/sm2005v196n03abeh000882
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发表时间：
2005-03-01
影响因子：
0.8
通讯作者：
Medvedev, KV
中科院分区：
文献类型：
--
作者：
Bogachev, VI;Kolesnikov, AV;Medvedev, KV
得到了Rn上测度的非线性象的熵的一个新恒等式，由此得到了著名的Talagrand不等式.研究了R-n和R-无穷域上的三角映射，即映射T使得第i个坐标函数Ti只依赖于变量x（1），. x（i）.借助于这样的映射，关于每个概率测度的可表示性的公知公开问题得到了肯定的解决，该概率测度相对于无限维空间上的高斯测度7是绝对连续的，作为在形式为T（x）= x + F（x）的映射下的伽马的像，其中F在测度伽马的Cameron-Martin空间中取值。作为应用，还证明了一个推广的对数Sobolev不等式.参考书目：23种。
A new identity for the entropy of a non-linear image of a measure on R-n is obtained, which yields the well-known Talagrand's inequality. Triangular mappings on R-n and R-infinity are studied, that is, mappings T such that the ith coordinate function T-i depends only on the variables x(1),., x(i). With the help of such mappings the well-known open problem on the representability of each probability measure that is absolutely continuous with respect to a Gaussian measure 7 on an infinite dimensional space as the image of gamma under a map of the form T(x) = x + F(x) where F takes values in the Cameron-Martin space of the measure gamma is solved in the affirmative. As an application, a generalized logarithmic Sobolev inequality is also proved. Bibliography: 23 titles.