抽象空间上的有向信息：性质与空间问题
Directed Information on Abstract spaces: Properties and Extremum Problems
摘要：
本文描述了一个框架，其中有向信息定义在抽象空间。利用Polish空间上概率测度的弱收敛拓扑，得到了有向信息的凸性、弱连续性、下连续性等性质。分析了与有记忆反馈信道容量有关的有向信息和非预期序列率失真的两个极值问题，分别给出了最大和最小分布的存在性。
英文摘要：
This paper describes a framework in which directed information is defined on abstract spaces. The framework is employed to derive properties of directed information such as convexity, concavity, lower semicontinuity, by using the topology of weak convergence of probability measures on Polish spaces. Two extremum problems of directed information related to capacity of channels with memory and feedback, and non-anticipative and sequential rate distortion are analyzed showing existence of maximizing and minimizing distributions, respectively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
