We use an information-theoretic argument due to O'Connell (2000) to prove that every sufficiently symmetric event concerning a countably infinite family of independent and identically distributed random variables is deterministic (i.e., has a probability of either 0 or 1). The i.i.d. condition can be relaxed. This result encompasses the Hewitt-Savage zero-one law and the ergodicity of the Bernoulli process, but also applies to other scenarios such as infinite random graphs and simple renormalization processes.

翻译：我们运用O'Connell（2000）提出的信息论论证方法，证明了对于可数无限个独立同分布随机变量构成的族，任何具有充分对称性的事件都是确定性的（即其概率非0即1）。该结论可放宽独立同分布的条件限制。此结果不仅涵盖了Hewitt-Savage零一律与伯努利过程的遍历性，同时适用于无限随机图及简单重整化过程等其他场景。