The Wiener Measure of Hilbert Neighborhoods in the Space of Real Continuous Functions
The Wiener Measure of Hilbert Neighborhoods in the Space of Real Continuous Functions
复制标题
实连续函数空间中希尔伯特邻域的维纳测度
DOI：
10.1002/sapm1944231195
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发表时间：
1944
期刊：
影响因子：
--
通讯作者：
W. T. Martin
中科院分区：
文献类型：
--
作者：
R. Cameron;W. T. Martin
导言。设C是在0：；t：上定义并连续的所有实值函数x(T)的空间。在他的关于广义Harmomc分析的论文中(其中引用了他的早期工作)N Wiener[1]在C中定义了一种测度，并根据这一测度定义了C上的积分，在考虑到空间C时，它具有勒贝格积分的许多常见性质。在一篇关于11on-Imar积分方程组的论文中，作者[2]证明了对于每个正数R，C的子集
Introduction. Let C be the space of all real-valued functIOns x (t) defined and contmuous on 0:::; t:::; 1 and vanishmg at t= O. In hIS paper on Generahzed Harmomc AnalysIs (in which references to his earlIer work are given) N Wiener [1] defines a measure in C and in terms of thIs measure he defines an mtegral over C which has many of the usual properties of the Lebesgue mtegral In the conSIderatIOn of the space C one frequently encounters the expreSSIOn [x2 (t) dt. In a paper on llon-Imear integral equations the authors [2] have shown that for every pOSItive number R the subset of C for which