Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations
Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations
复制标题
使用某些 Sturm-Liouville 微分方程评估各种维纳积分
DOI：
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发表时间：
1945
期刊：
影响因子：
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通讯作者：
W. T. Martin
中科院分区：
文献类型：
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作者：
R. Cameron;W. T. Martin
乘数之前的积分已被如此选择，使整个空间C的措施等于单位。有了这个准区间测度的定义，C上的维纳测度可以用完全类似于普通勒贝格测度的方式定义，并且可以定义C上的（维纳）积分理论，泛函F[x]的积分是一个数。我们写
the multiplier before the integrals having been so chosen as to make the measure of the entire space C equal to unity. With this definition of measure for quasi-intervals, the Wiener measure on C can be defined in a manner entirely similar to that used for ordinary Lebesgue measure, and a theory of (Wiener) integration can be defined over C, the integral of a functional F[x] being a number. We write