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I've seen "the Pacman lemma" mentioned in the context of reduction orderings on logical terms, but a Google search doesn't find a definition; what exactly is it? Closest a search found was a "Pacman rule" in the context of calculus; is that the same thing?

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up vote 5 down vote accepted

Lemma. : Let $(X,\mathcal{S})$ be a measurable space, $\nu$ a signed measure. Suppose we have a subset $E \in \mathcal{S}$ and $0 < \nu(E) < \infty$ . Then, there exists a positive set $P \subset E$ such that $\nu(P) > 0$.

I found it here:

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Why is this called the Pacman lemma? (For every E of positive measure there exists a positive set that "eats" it?(??)) – ShreevatsaR May 25 '11 at 7:55
Who knows? I had never heard of it, until i searched in Google :) – user9413 May 25 '11 at 8:14
@ShreevatsaR: I guess it's in the proof. Eat all the really big negative subsets (nuggets) and whatever remains, as improbable as it seems, must be positive. Elementary, dear Watson! – t.b. May 25 '11 at 11:12

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