In measure theory, we have "lambda systems" and "pi systems". Pearl's message passing algorithm has "lambda messages" and "pi messages". Is there a reason that lambda and pi go together?
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
The measure theory ideas of $\pi$-system and $\lambda$-system were introduced by Dynkin in his book Die Grundlagen der Theorie der Markoffschen Prozesse (1961 German translation of 1959 Russian original); a note at the end of the book mentions they are new, but doesn't explain why they are so called. My guess has been that $\pi$ is for "product" and $\lambda$ is for "limit," or some Russian cognates thereof; I'm not sure there's any connection between the letters themselves. Although Professor Dynkin has recently retired, he still has an office here at Cornell; if I see him and I think of it, I may ask him about it.
Unfortunately I don't know anything about message passing, so I can't say whether Pearl's terminology is related or a coincidence.