States of classical statistical mechanical systems of infinitely many particles. I
States of classical statistical mechanical systems of infinitely many particles. I
复制标题
无限多个粒子的经典统计力学系统的状态。
DOI：
10.1007/bf00251601
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发表时间：
1975
影响因子：
2.5
通讯作者：
A. Lenard
中科院分区：
文献类型：
--
作者：
A. Lenard
我们研究了无限多个点粒子经典系统的一般数学模型。无限粒子构型的空间X具有自然拓扑以及与之相关的可测结构。它还与单粒空间E中以有界开集A为指标的有限构形局部空间族{XA}相联系.证明了一个类似于Kolmogoroff随机过程基本定理的定理.根据这个定理，定义在XA上的相容的一族局部概率测度μA产生了X上唯一的概率测度μ.我们还研究了定义在X上的某些实函数的线性空间上的正线性形式的积分表示问题.我们证明了定义在C+P类中的函数f的正线性形式F(F)，允许唯一确定的积分表示F(F)=∝f(ξ)dμ，其中μ是X上的概率度量。
We study a general mathematical model of a classical system of infinitely many point particles. The space X of infinite particle configurations is equipped with a natural topology as well as a measurable structure related to it. It is also connected with a family {XA} of local spaces of finite configurations indexed by bounded open sets A in the one-particle space E. A theorem analogous to Kolmogoroff's fundamental theorem for stochastic processes is proved, according to which a consistent family {μA} of local probability measures μAdefined on the XAgives rise to a unique probability measure μ on X. We also study the problem of integral representation for positive linear forms defined over some linear space of real functions on X. We prove that a positive linear form F(f), defined for functions f in the class C+P, admits a uniquely determined integral representation F(f)=∝ f (ξ) dμ, where μ is a probability measure over X.