1. The problem statement, all variables and given/known data Let A1,A 2,...be an inﬁnite sequence of events such that A1⊂A2⊂.... Prove that Pr(∪Ai)=limn→infPr(An) ∪ is also an iterator that starts from i=1 to infinity. How can you put those iterators? 2. Relevant equations I decided to use induction 3. The attempt at a solution Proof by induction Base case let A1⊂A2 so A1∪A2=A2 Therefore Pr(A1∪A2)=Pr(A2) Inductive Step let Pr(∪Ai)=limk→infPr(Ak) then we have to show that if Ak⊂Ak+1 then limk→infPr(Ak∪Ak+1)=limk→infPr(Ak+1) so This is true because Ak∪Ak+1=Ak+1 so limk→infPr(Ak∪Ak+1)=limk→infPr(Ak+1) so by math induction Pr(∪Ai)=limn→infPr(An) is that right?