2Probabilistic Preliminaries
From this chapter on,, and we will connect them to formal concepts.
In this chapter, we will make the first steps toward measure‐theoretic probability, and we will construct some basic stochastic processes of theoretical importance. We assume that the reader is somewhat familiar with elementary probability calculus. To remind, the elementary probability calculus deals with probability on countable spaces of possible outcomes. If we have a collection of certain elementary events 
, where set 
is countable, we can define a discrete probability distribution 
as an arbitrary function such that 
for each 
and 
. The underlying idea is that we find the finest partition of the space of interest, and we define the probability distribution for the smallest elements of this space.
The above approach leads to many important intuitions about probability and works well for ...
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