After picking an appropriate state-space to work in, we'll need to construct
another vector space ``above'' it. This will be the space of all
random variables taking on values in our state space. We will
denote this space 
and prove it a Hilbert Space. In other words, we're building the
space which contains the probabalistic elements we're constructing our model system with. In
this space we will be able to describe the statistical, causal relationships between random
variables in terms of geometry, which is really neat.