Consider the measurable space $(\Omega,\mathcal{F})$ where $\Omega$ is the sample space and $\mathcal{F}$ is the a set of observable events. Further assume that we are estimating a linear regression $GDP_i=\alpha+\beta_1 POP_i+\beta_2 TECH_i+\epsilon$ where the dependent variable is GDP of a country and independent variables are population and some measure of technology.
The question is how do I formalize this problem in measure-theoretic probability theory? More specifically, what would be the sample space, $\Omega$ in this test? (I am thinking along the lines of it being the set of all possible countries in the world, but what exactly are those?)
EXAMPLE
If we are talking about a coin toss experiment where we toss the coins twice, then our sample space is $\{HH,HT,TT,TH\}$. So my question is in modeling GDP in countries, what is our sample space.