Explore a seminar on theoretical machine learning focusing on learning probability distributions and their limitations. Delve into the fundamental statistical learning problem, examining the most ambitious framework and its proven impossibility. Discover density estimation of restricted distribution families and sample compression schemes as key technical tools. Investigate various examples of EMX problems, including binary classification and subset probability maximization. Analyze the "Fundamental Theorem of Statistical Learning" and its implications. Examine non-equivalence for EMX, monotone compression techniques, and quantitative versions of these concepts. Gain insights into model theoretic observations and discuss new challenges in the field of probability distribution learning.