标准Borel空间中的经验过程、典型序列与协调行动
Empirical processes, typical sequences and coordinated actions in standard Borel spaces
摘要：
本文提出了一类抽象字母表（所谓的标准Borel空间）上的典型序列的新概念，它基于无记忆源在一类可测“测试函数”上的经验分布的一致逼近.在有限字母表的情况下，我们可以取所有一致有界的函数，并恢复通常的强典型性（或全变差距离下的典型性）概念。然而，对于一般的字母表，这个函数类太大了，必须加以限制。考虑到这一点，我们定义了关于任何Glivenko-Cantelli函数类的典型性（即，一个函数类，承认一个统一的大数定律），并证明其权力，通过给出简单的推导的基本限制的可实现的速率在几个信源编码的情况下，其中有关的操作标准涉及到再生经验平均的一般字母固定无记忆源相对于一个合适的函数类。
英文摘要：
This paper proposes a new notion of typical sequences on a wide class of abstract alphabets (so-called standard Borel spaces), which is based on approximations of memoryless sources by empirical distributions uniformly over a class of measurable "test functions." In the finite-alphabet case, we can take all uniformly bounded functions and recover the usual notion of strong typicality (or typicality under the total variation distance). For a general alphabet, however, this function class turns out to be too large, and must be restricted. With this in mind, we define typicality with respect to any Glivenko-Cantelli function class (i.e., a function class that admits a Uniform Law of Large Numbers) and demonstrate its power by giving simple derivations of the fundamental limits on the achievable rates in several source coding scenarios, in which the relevant operational criteria pertain to reproducing empirical averages of a general-alphabet stationary memoryless source with respect to a suitable function class.
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