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Law of total probability and Bayes' theorem in Riesz spaces

Measure-free probability theory

Cite as:

Liang Hong (2018). Law of total probability and Bayes' theorem in Riesz spaces. RESEARCHERS.ONE, https://www.researchers.one/article/2018-10-3.

Abstract:

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.