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Starting with simple examples of rolling dice and flipping coins, probability spaces and general measure spaces are introduced together with their measure theoretic background. Basic properties of measures and probability measures are shown. After introducing the concept of independence for a family of events and Bayes’ rule, it is demonstrated how the lemma of Fatou for sets and the lemma of Borel-Cantelli can be derived.

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Measure Spaces and Probability Spaces

  • 章节

  • 发表日期：

    2025年

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  • Hannah Geiss,
  • Stefan Geiss

摘要

Starting with simple examples of rolling dice and flipping coins, probability spaces and general measure spaces are introduced together with their measure theoretic background. Basic properties of measures and probability measures are shown. After introducing the concept of independence for a family of events and Bayes’ rule, it is demonstrated how the lemma of Fatou for sets and the lemma of Borel-Cantelli can be derived.