Let A be a o-algebra on E and FC E. Show that TP:= {An F, A...

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Let A be a o-algebra on E and FC E. Show that TP:= {An F, A E A}, is a o-algebra on F (called trace o-algebra). 1. Let A be the o-algebra generated by (Sn)nez, where Sn = {n, n+1.n+2}. Prove that A= P(Z). 2. Find the o-algebra in R generated by A={10,2],[1,3]} Let A be a o-algebra on E and FC E. Show that TP:= {An F, A E A}, is a o-algebra on F (called trace o-algebra). 1. Let A be the o-algebra generated by (Sn)nez, where Sn = {n, n+1.n+2}. Prove that A= P(Z). 2. Find the o-algebra in R generated by A={10,2],[1,3]}

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To prove that TF A F A A is an algebra on F we need to show that it satisfies the three properties of a algebra it contains the whole set F is closed under complementation and is closed under countabl... View the full answer