ABSTRACT
In this chapter we want to develop the foundations of sample theory. First assume that we want to make an inference, either estimation or some test, based on a sample. We are interested in how well parameters or statistics based on that sample represent the parameters or statistics of the whole population.
In statistical terms, we want to develop the concept of convergence. Specifically, we are interested in whether or not the statistics calculated on the sample converge toward the population values. Let {Xn} be a sequence of samples. We want to demonstrate that statistics based on {Xn} converge toward the population statistics for X.
