关于过程可测性的一个注记

A Note on Measurability of Process

利用测度论工具对随机过程进行深入的研究时 ,往往需要假设随机过程具有某种可测性 .为了从另一个角度说明这个假设的必要性 ,构造一类不可测的但在任意时刻都以概率 1为 0的随机过程 ;

For deepgoing study of stochastic processes by measure theory,a hypothesis that stochastic processes possess some measurability is often required. In order to illustrate necessity of the hypothesis from another angle,a unmeasurable process which equals to 0 almost everywhere for any fixed time is given.Furthermore,using the method of spaces union,it is proved that it is impossible to getmeasurability from just finite dimensional distribution class.