n the chapter (
) we introduced notions of random events and
illustrated how statements about realization of random variables could be
treated as operations on sets and measured via probability function defined on
these sets. In the present chapter we expand such approach.
The references for this chapter are
is called "probability space". Here the
is an event space,
of subsets of
(see the section
Operations on sets and
is a probability measure (p.m.)
is the Borel field with
is a minimal
containing all open sets.
(Borel measurable function) The mapping
is a "Borel measurable function"
The random variable
induces the triple
according to the
For a measure
we introduce a (cumulative) distribution function (d.f.)