Suppose that Ω = [0,1] is the unit interval, and F is the set of all subsets A such that either A or Ac is finite, and P is defined by P(A) = 0 if A is finite, and P(A) if Ac is finite.
Show that F is an algebra:Show that F is not a σ-algebraShow that P is finitely additive:Show that P is countably additive on F