I've just started measure theory and I'm really struggling with what's supposed to be easy proofs. Any help would be appreciated.
1.1) Let be a sequence of subsets of X. Prove that
1.2) Let be a sequence of subsets of X. Prove that
I attempted to do this using the definition of limsup and liminf (for limsup. x belongs to limsup if it belongs to infinitely many E_n and y belongs to liminf if it belongs to all but finitely many E_n) but my professor said to rather do it using set inclusion that is if x belongs to limsupE_n then x belongs to and if y belongs to then y belongs to limsup E_n. I started by assuming and where do I go from here?