proof of Borel-Cantelli 1
Let be the event for . If is in the event ’s i.o., then for all . So .
Conversely, if for all , then we can show that is in ’s i.o. Indeed, means that for some . However implies that for some that is strictly larger than . Thus we can produce an infinite sequence of integer such that for all .
Let be the event . We have
|Title||proof of Borel-Cantelli 1|
|Date of creation||2013-03-22 14:28:16|
|Last modified on||2013-03-22 14:28:16|
|Last modified by||kshum (5987)|