efinition
(Limsup and liminf for sets)
;
;
Definition
.
The "i.o." stands for "infinitely often".
Proposition
(BorelCantelli lemma, part 1).
.
Proposition
(IO criteria for AS convergence)
For a sequence of r.v.
the following are equivalent statements:
1.
a.s.
2.
,
