The I-Measure
The I-Measure
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DOI：
10.1007/978-1-4419-8608-5_6
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
R. Yeung
中科院分区：
文献类型：
--
作者：
R. Yeung
在第二章中，我们用图2.2给出了两个随机变量的Shannon信息测度之间的关系。为了方便起见，图2.2在图6.1中再现，其中随机变量X和Y分别被X1和X2代替。这张图表明，任何n：2：2随机变量的香农信息测度可能有一个集合论的结构。在本章中，我们发展了一个理论，它建立了香农信息测度和集合论之间的一对一的对应关系。有了这种对应关系，香农信息测度的操作可以被视为集合运算，从而允许集合论中丰富的工具套件被用于信息论。此外，香农的信息测度的结构可以很容易地通过一个
In Chapter 2, we have shown the relationship between Shannon's infonnation measures for two random variables by the diagram in Figure 2.2. For convenience, Figure 2.2 is reproduced in Figure 6.1 with the random variables X and Y replaced by Xl and X2, respectively. This diagram suggests that Shannon's information measures for any n: 2: 2 random variables may have a set-theoretic structure.In this chapter, we develop a theory which establishes a one-to-one correspondence between Shannon's information measures and set theory in full generality. With this correspondence, manipulations of Shannon's infonnation measures can be viewed as set operations, thus allowing the rich suite of tools in set theory to be used in information theory. Moreover, the structure of Shannon's information measures can easily be visualized by means of an