The article explores how to find a simpler measure that closely approximates a complex probability distribution on an infinite-dimensional space. By using the Kullback-Leibler divergence as a measure of similarity, the researchers focus on Gaussian measures and establish basic theorems on their existence and uniqueness. They introduce a parameterization method for Gaussians and explain the importance of regularization in the approximation process. The study provides a framework for developing computational algorithms to efficiently approximate complex probability distributions.