Closedness of Sum Spaces andthe Generalized Schrödinger Problem
Closedness of Sum Spaces andthe Generalized Schrödinger Problem
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和空间的封闭性与广义薛定谔问题
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
W. Thomsen
中科院分区：
文献类型：
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作者：
L. Rüschendorf;W. Thomsen
建立了可测函数和空间的一般闭性。作为应用，在可积性条件下，在没有任何拓扑或有界性假设的情况下，得到了广义Schr odinger问题解的存在唯一性结果.他们还允许证明一个有趣的结构结果的分布与多元边际，证明存在结果的最佳近似在添加剂统计模型，并给出了一个扩展的Kolmogorov的表示定理连续函数的severalvariables。这种扩展意味着任何局部有界的可测函数都可以通过一个具有一个隐藏层的神经网络进行精确表示。
Some general closedness properties of sum spaces of measurable functions are established. As application one obtains existence and uniqueness results for solutions of the generalized Schr\"odinger problem under an integrability condition but without any topological or boundedness assumptions. They also allow to prove an interesting structural result for distributions with multivariate marginals, to prove existence results for optimal approximations in additive statistical models, and to give an extension of Kolmogorov's representation theorem for continuous functions of severalvariables. This extension implies that any locally bounded measurable function has an exact representation by a neural network with one hidden layer.