When presented with an arbitrary measure metric space, one often would like to use the classic results of Euclidean analysis, but one does not have the necessary structure. As an approach around this setback, many mathematicians impose new constraints on the space. Requiring that a metric measure space has a doubling measure and supports a Poincaré inequality allows for analysis from many fields of mathematics to be explored on this space. In this talk, I will present the desirable consequences of a space $(X,d,\mu)$ that has a doubling measure and supports a $p$-Poincaré inequality. I will then discuss a necessary and sufficient condition for $X$ to support a $p$-Poincaré inequality, that uses discretizations of $X$ to form an approximating sequence of graphs. This results provides a computationally easier route to verifying if an arbitrary space supports a $p$-Poincaré inequality.