e study various convergence concepts for sequences of random variables
where
is an event space often identified with
.
We will be frequently using the notation and techniques of the section
(
operations on sets
).
The random variables are always assumed to be
measurable
for some
-algebra
:
or,
equivalently,
In practical language these mean the following. The complete description of
the world is given by the set
.
The statements about the world are given by subsets of
.
Some amount of information (unknown at present but will be known in the
future) is represented by the algebra
.
This information
has to be an algebra of sets because we will be making logical statements and
derivations about our knowledge, see the section
(
operations on sets
). We restrict
our attention to the random variables that become deterministic if the
information
is given. Equivalently,
contains all the randomness in the variables under consideration.
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