et
be a probability measure,
for a
algebra
.
An
measurable
random variable
:
gives rise to the set function
given by the
relationship
The measure
does not have to be positive or normalized to 1. This brings us to
consideration of a wider class of measures.
Proof
Using the notation of the previous proposition set
and
.
Definition
The measure
is called "total variation" or "absolute value" of
.
