Contributions to information theory for abstract alphabets
Contributions to information theory for abstract alphabets
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对抽象字母信息论的贡献
DOI：
10.1007/bf02592011
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发表时间：
1961
期刊：
影响因子：
--
通讯作者：
A. Tulcea
中科院分区：
文献类型：
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作者：
A. Tulcea
本文以B为中心给出了一些结果。信息论中的麦克米伦定理本文采用A. [9]和[10]。在W1中，我们证明了一些初步结果。主要定理在W 2中给出。它们处理p阶的平均收敛（其中1< p<~），由L中的函数控制，以及几乎处处收敛。w3专门发表各种评论和意见。特别是，它表明在这里，各种经典定理从信息论有限字母表的特殊情况下，本文证明的结果。附录包含了一个简短而直接的证明，证明了在有限字母表的情况下，几乎处处收敛在麦克米兰定理中成立（本质上，这也是从一般定理1得出的）。
In this paper we give some results centering around B. McMillan's theorem in information theory. The paper is presented in the abstract setting developed by A. Perez in [9] and [10]. In w 1 we prove some preliminary results. The main theorems are given in w 2. They deal with mean convergence of order p (where 1< p<~), domination by a function in L, as well as convergence almost everywhere. w 3 is devoted to various remarks and comments. In particular, it is shown here that various classical theorems from information theory for finite alphabets are particular cases of the results proved in this paper. The appendix contains a short and direct proof of the fact that (essentially, this follows also from the general theorem 1), in the case of a finite alphabet, the almost-everywhere convergence holds in McMillan's theorem.
DOI：
10.1002/9781118231296.ch8
发表时间：
2018-11
期刊：
Gauge Integral Structures for Stochastic Calculus and Quantum Electrodynamics
影响因子：
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作者：
Dr. Gergely Záruba
通讯作者：
Dr. Gergely Záruba