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1. boole 's inequality, sure sets, null sets and borel-cantelli a) Prove Boole's inequality, that for any n E NUoo) b) Hence, verify that the countable union of any collection of null sets is still a null set: P(Nk) 0 V k E N PlupNk) = 0. c) Hence, or otherwise, show that the countably infinite intersection of sure sets remains sure: P(SJ-1 n ...
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