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Oct 19, 2009 at 18:20 comment added Theo Johnson-Freyd Cool. I'm not too surprised by the results --- without all the model theory they are in Schanuel. What I was asking about integration is this: on a compact Riemannian, there is a (smooth) measure described in terms of curvature of the manifold whose total integral is the euler characteristic, but we can also use it as a natural measure on the manifold for integrating other functions. I don't know (and the papers I cited don't say, but I'll check out your paper) a natural "measure" on R whose total integral is -1. Given the Chen/Rota definition, I'd expect it to concentrated near the ends.
Oct 19, 2009 at 18:15 vote accept Theo Johnson-Freyd
Oct 19, 2009 at 10:08 history answered Robert Ghrist CC BY-SA 2.5