Consider the set function ℙ defined for every subset of [0, 1) by the formula that ℙ (A) = 0 if A is a finite set and ℙ (A) = ∞ if A is an infinite set

Consider the set function ℙ defined for every subset of [0, 1) by the formula that ℙ (A) = 0 if A is a finite set and ℙ (A) = ∞ if A is an infinite set. Show that ℙ satisfies (1.1.3)-(1.1.5), but ℙ does not have the countable additivity property (1.1.2). We see then that the finite additivity property (1.1.5) does not imply the countable additivity property (1.1.2).