Probability Space
The setup of a random experiment. It can be defined as the tuple
Where:
: The set of all possible outcomes of the experiment
: A set containing subsets of , each element in
are called Events
: a function 
that satisfies the following properties
1. 
2. 
3. 
for 
and disjoint events 
contains all the basic outcomes of the event, as well as
combinations of them. For example for a basic die throw, would be
. would for example contain 
, which
is the event that the die would land on a 2, it could also contain
combinations like 
which denote the event of the die landing on
an even number. It is up to us to define as we want. If we
want to be able to reason about every possible combinations of outcomes,
we can set 
where 
is the Powerset
of .