Abstract
Let A1, ℬ, A2 be σ-algebras of events having the following relationship: if the outcomes of all events in ℬ are known, events A2 ∈A2 are independent of events A1 ∈ A1. More precisely, the σ-algebras A1 and A2 are conditionally independent with respect to ℬ; this gives the equation for conditional probabilities:
for any A1 ∈ A1, A2 ∈A2. We say that the σ-algebra ℬ splits A1 and A2 (or is splitting) if (1.1) holds for A1, ℬ, A2.
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© 1982 Springer-Verlag New York Inc.
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Rozanov, Y.A. (1982). Markov Random Fields. In: Markov Random Fields. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8190-7_2
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DOI: https://doi.org/10.1007/978-1-4613-8190-7_2
Publisher Name: Springer, New York, NY
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