When this quantity is infinite, Vitali’s theorem states that the convergence of a sequence of functions implies the existence of uniformly absolutely continuous integrals. If A has a positive value for this quantity and an arbitrary subset B has a zero value for this quantity, then A is called an atom. This quantity for a countable union of sets is less than or equal to the sum of this quantity over each individual set due to the property of (*) subadditivity. Functions involving this quantity are defined over sigma-algebras. It’s not cardinality, but this quantity is always zero for an empty set. For any closed or open interval from a to b, the Lebesgue form of this quantity is b minus a. For 10 points, name this quantity that yields the “size” of a set, examples of which include length, area, and volume. ■END■
ANSWER: measure [accept Lebesgue measure; prompt on mu or m]
<Ezra Santos, Other Science>
= Average correct buzz position