论文标题
在上限和下限上，事件组合的概率
On upper and lower bounds for probabilities of combinations of events
论文作者
论文摘要
我们从$ n $事件发生的$ r $或至少$ r $的概率中得出了新的上限和下限。这些界限可以转向平等。也讨论了该方法。它也适用于可衡量的空间和标志的措施。我们还讨论了结果的有条件概率，以上述事件给定$σ$ - 场。从两个不平等方面的有条件概率的期望中，无条件的概率可能会产生更好的界限。
We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also discuss variants of the results for conditional probability of above events given $σ$-field. Taking expectations from both parts of inequalities for conditional probabilities can yield better bounds for unconditional ones.
