We study the problem of sequentially predicting properties of a probabilistic model and its next outcome over an infinite horizon, with the goal of ensuring that the predictions incur only finitely many errors with probability 1. We introduce a general framework that models such prediction problems, provide general characterizations for the existence of successful prediction rules, and demonstrate the application of these characterizations through several concrete problem setups, including hypothesis testing, online learning, and risk domination. In particular, our characterizations allow us to recover the findings of Dembo and Peres (1994) with simple and elementary proofs, and offer a partial resolution to an open problem posed therein.

翻译：我们研究了在无限时间范围内，对概率模型的属性及其下一个结果进行序贯预测的问题，目标是确保预测以概率1仅产生有限次错误。我们引入了一个通用框架来建模此类预测问题，为成功预测规则的存在性提供了通用刻画，并通过若干具体问题设置（包括假设检验、在线学习和风险主导）展示了这些刻画的应用。特别地，我们的刻画能以简单而初等的方式重现Dembo和Peres（1994）的发现，并部分解决了其中提出的一个开放问题。