Let C[0, T] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. For a partition \(0=t_0<t_1<\cdots <t_n=T\) of [0, T], define \(X:C[0,T]\rightarrow \mathbb R^{n+1}\) by \(X(x)=(x(t_0),x(t_1),\ldots ,\)\(x(t_n))\). In this paper, we derive a simple evaluation formula for Radon–Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function X which has a drift and an initial weight. As applications of the formula, we evaluate the Radon–Nikodym derivatives of the functions \(\int _0^T[x(t)]^m\mathrm{d}\lambda (t)(m\in \mathbb N)\) and \([\int _0^Tx(t)\mathrm{d}\lambda (t)]^2\) on C[0, T], where \(\lambda \) is a complex-valued Borel measure on [0, T].

令C [0，  T ]表示维纳空间的类似物，即间隔[0，T ]上的实值连续函数的空间 。对于[0，  T ]的分区\（0 = t_0 <t_1 <\ cdots <t_n = T \），定义\（X：C [0，T] \ rightarrow \ mathbb R ^ {n + 1} \）通过\（X（x）=（x（t_0），x（t_1），\ ldots，\）\（x（t_n））\）。在本文中，我们推导了Radon-Nikodym衍生物的简单评估公式，类似于条件函数X对C [0，  T ]的函数的条件期望。具有漂移和初始重量。作为公式的应用，我们评估函数\（\ int _0 ^ T [x（t）] ^ m \ mathrm {d} \ lambda（t）（m \ in \ mathbb N）\的Radon-Nikodym导数）和C [0，  T ]上的\（[\ int _0 ^ Tx（t）\ mathrm {d} \ lambda（t）] ^ 2 \），其中\（\ lambda \）是复数值的Borel度量在[0，  T ]上。