Bonferroni inequalities are a set of mathematical inequalities that provide bounds for the probabilities of unions of events, helping to manage the risk of type I errors in statistical tests. These inequalities are particularly useful when dealing with multiple hypotheses, as they allow statisticians to adjust the significance level to control the probability of false positives. They connect deeply with foundational concepts like probability spaces and axioms, as they rely on understanding events and their probabilities within those spaces.
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