A Wald-like equation is proved for the entropy of a randomly stopped sequence of independent identically distributed discrete random variables X/sub 1/, X/sub 2/. . ., with a nonanticipating stopping time N. The authors first define a general stopping time and the associated stopped sequence, and then present the two main theorems for the entropy of a stopped sequence. The formal proofs of the lemmas necessary for the proof of the theorems are given. The randomness in the stopped sequence X/sup N/ is the expected number of calls for X times the entropy per call plus the residual randomness in the stopping time conditioned on the unstopped sequence X/sup infinity /.
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机译：证明了一个Wald-like方程，证明了独立同分布离散随机变量X / sub 1 /，X / sub 2 /的随机停止序列的熵。 。作者首先定义了一个一般的停止时间和相关的停止序列，然后给出了停止序列的熵的两个主要定理。给出了定理证明所必需的引理的形式证明。停止序列X / sup N /中的随机性是X的预期呼叫数乘以每个呼叫的熵再加上以未停止序列X / sup infinity /为条件的停止时间中的剩余随机性。
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