This note generalizes the notion of conditional probability to Riesz spaces using the order-theoretic approach. With the aid of this concept, we establish the law of total probability and Bayes' theorem in Riesz spaces; we also prove an inclusion-exclusion formula in Riesz spaces. Several examples are provided to show that the law of total probability, Bayes' theorem and inclusion-exclusion formula in probability theory are special cases of our results.
➤ Version 1 (2018-10-03)
Liang Hong (2018). Law of total probability and Bayes' theorem in Riesz spaces. Researchers.One, https://researchers.one/articles/law-of-total-probability-and-bayes-theorem-in-riesz-spaces/5f52699b36a3e45f17ae7d7c/v1.