8Zero‐One Laws
If an event depends on a sequence
of random variables, and
is its probability after
are known, then, almost surely,
tends to 1 if
happens and to 0 if not. More generally, if an integrable random variable
is a function of
, and
is its expected value after
are known, then
tends almost surely to . This is Lévy's classical zero‐one law, roughly as he stated it in 1937 [245, section ...
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