Abstract: The connection between finitely additive probability measures and NIP theories was first noticed by Keisler. Around 20 years later, the work of Hrushovski, Peterzil, Pillay, and Simon greatly expanded this connection. Out of this research came the concept of generically stable measures. In the context of NIP theories, these particular measures exhibit stable behavior. In particular, Hrushovski, Pillay, and Simon demonstrated that generically stable measures admit a natural finite approximation. In this talk, we will discuss generically stable measures in the local setting. We will describe connections between these measures and concepts in functional analysis as well as show that this interpretation allows us to derive a local approximation theorem.