Sanov's Theorem is a fundamental result in information theory and statistics that describes the asymptotic behavior of empirical distributions. It states that, as the sample size increases, the probability of observing a distribution that significantly deviates from a given reference distribution decreases exponentially. This theorem is particularly useful in understanding how well a sample represents a population. The theorem is often applied in the context of large deviations and statistical inference. It provides a way to quantify the likelihood of rare events and helps in estimating the performance of statistical models. Overall, Sanov's Theorem is essential for analyzing the convergence of empirical measures to their expected distributions.