Caturday Post: Scaramouche Is A Measurable Set*

But he might chew on the measuring instrument.

*That is, we can apply to him a non-negative real function m such that
   1) m(empty set) = 0
   2) for any finite or countable collection of pairwise disjoint sets A_n in Scaramouche with the union of the A_n's = A also in Scaramouche, the sum over n of the m(A_n) = m(A). (i.e., measuring all the little pieces and adding is the same as adding all the little pieces and then measuring, since we are assuming that none of the pieces overlap: that's the pairwise disjoint bit). 

For further reading on measures, Wolfram Mathworld is always helpful.