Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
1  
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 mathoverflow.net/questions/30081/… –  Arturo Magidin Sep 14 '10 at 19:58
add comment

1 Answer

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.

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.