论文标题
量度理论和应用中有限加性功能
Finitely additive functions in measure theory and applications
论文作者
论文摘要
我们在给定的Sigma-Algebra的子集上考虑并确切地将ra子 - 尼克比衍生物算子的一定延伸到添加剂但不一定是sigma addive的函数。我们为概率理论提供了应用；特别是，要研究$ $ $ - 布朗尼运动，通过广义的ITô-Integrals及其伴随（以广义随机导数的形式），以$ $ $ $ $ $ $的家族索引的转型概率运算符系统，以及组成运营商的伴侣。
We consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability theory; in particular, to the study of $μ$-Brownian motion, to stochastic calculus via generalized Itô-integrals, and their adjoints (in the form of generalized stochastic derivatives), to systems of transition probability operators indexed by families of measures $μ$, and to adjoints of composition operators.
