ABSTRACT
Averaging is a different kind of operation since it associates with a stochastic
variable a non-stochastic or “sure” number. Alternatively it may be viewed as
a projection in the following way. The set of all stochastic variables contains
a subset of variables whose probability density is a delta peak. This subset is
isomorphic with the sure numbers of the range and may therefore be identified
with them. The operation of taking average is then a projection of the total
space of stochastic variables onto this subset.
