[JadeNB]

> Measure theory is the branch of mathematics concerned with developing new notions of size appropriate to different contexts.

While this is probably among the most interesting definitions I've ever seen, I'm not sure it is correct. Cardinality, as we've discussed it here, is usually considered to be in the domain of set theory; measure theory assigns measures in a multitude of interesting ways, but, at least in all of it with which I'm familiar, those measures come only from [0, ∞], not from some more exotic domain of values. (A lot of the measure-theory proofs that I know do rely in this being the set of values of a measure—for example, on being able to subtract most of the time, and on having only one kind of infinite measure—so just saying "let's allow different values" doesn't immediately rescue it.)