General Entropy of General Measures
General Entropy of General Measures
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一般测度的一般熵
DOI：
10.1142/s0218488502001442
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
A. Dukhovny
中科院分区：
文献类型：
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作者：
A. Dukhovny
熵的概念是加性测度理论的重要组成部分。在本文中，引入了一般（不一定是加性）测度的熵定义，作为“从属”加性测度的香农熵的无穷大。讨论并证明了一般熵的几个性质。某些性质要求该测度属于本文介绍和研究的所谓“等熵”一般测度类别。将广义熵的定义推广到可数情况，并证明了收敛的充分条件。我们引入了一般测度的“条件组合”方法，并证明了在这种情况下一般熵具有“子集独立”性质。
The concept of entropy is an important part of the theory of additive measures. In this paper, a definition of entropy is introduced for general (not necessarily additive) measures as the infinum of the Shannon entropies of "subordinate" additive measures. Several properties of the general entropy are discussed and proved. Some of the properties require that the measure belongs to the class of so-called "equientropic" general measures introduced and studied in this paper. The definition of general entropy is extended to the countable case for which a sufficient condition of convergence is proved. We introduce a method of "conditional combination" of general measures and prove that in that case the general entropy possesses the "subset independence" property.