论文标题
{在$ \ textbf {c} [0，\ infty）上直接构造了维纳措施
{A direct construction of the Wiener measure on $\textbf{C}[0, \infty)$
论文作者
论文摘要
Our construction of the Wiener measure on $\textbf{C}=\textbf{C}[0, \infty)$ consists in first defining a set function $φ$\ on the class of all compact sets based on certain $n$-dimensional normal distributions, $n = 1,\ 2,\ldots$\ using the structural relation at (\ref{E1.2}) below.这一由第一作者发现的结构关系在他的书（2013）的第130页上记录下来。然后，我们在borel $σ$ field上定义了$ \ textbf {c} $的亚集的量子$μ$，这是维纳尔措施。这是通过$ \ textbf {c} _a = \ textbf {c} [c} [0，a）上的Wiener Measure的类似结构完成的，其中$ a> 0 $是任意的实际号码。 传统的方法是首先构建布朗运动过程（BMP），然后证明它是可测量的映射到$（\ textbf {c}，\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ iffty）$，请调用$ \ textbf {c} $ \ wener的un $ \ fextbf {c} $ \ the wiener Measure the $ \ textbf {c} $ \。在本文中，我们直接定义了维纳措施。
Our construction of the Wiener measure on $\textbf{C}=\textbf{C}[0, \infty)$ consists in first defining a set function $φ$\ on the class of all compact sets based on certain $n$-dimensional normal distributions, $n = 1,\ 2,\ldots$\ using the structural relation at (\ref{E1.2}) below. This structural relation, discovered by the first author, is recorded in his book (2013) on page 130. We then define a measure $μ$ on the Borel $σ$-field of subsets of $\textbf{C}$ which is the Wiener measure. This is done via a similar construction of the Wiener measure on $\textbf{C}_a=\textbf{C}[0, a)$ where $a > 0$ is an arbitrary real number. The traditional way is to first construct the Brownian Motion process (BMP) and then, by proving it is a measurable mapping into $(\textbf{C},\ \mathscr{C}_\infty)$, call the measure induced by the BMP on $\textbf{C}$\ the Wiener measure. In the present paper, we define the Wiener measure directly.
