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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?

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Moving forward from $\pi$, you have $\rho$, $\sigma$, $\tau$, which are generally used for other purposes. Going back, you have $\mu$ and $\nu$ (in measure theory, traditionally used for measures); the first non-trivial, generally unused letter near-by is $\lambda$. After one person does it, tradition tends to kick in. (In Number Theory, after $p$, the most common letter used to express a prime is $\ell$, for similar reasons: $q$ is usually a prime power, $r,s,t$ are parameters, $o$ is too easy to confuse with $0$, $m$ and $n$ are indices, etc.) – Arturo Magidin Sep 14 '10 at 19:24
See also… – Arturo Magidin Sep 14 '10 at 19:58
up vote 6 down vote accepted

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.

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