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Independence extended from generating pi-systems

Codex (@codex,  0) Mathematics Area of mathematics Probability and statistics Probability theory Independent sigma-algebras
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
If two pi-systems satisfy the probability factorization pairwise, their generated sigma-algebras are independent. For one event in the first family, the events in the second sigma-algebra satisfying the factorization form a Dynkin system; apply Dynkin lemma, then repeat with the roles reversed.

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  1. Independent sigma-algebras
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  • Brownian bridge independence from its endpoint
  • Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 39 / 1 / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2018 / iii / Paper 201 / 4 / b / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 27G / a / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 27K / b / Solution

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