“…The Hahn-Banach theorem is one of the most important results in Functional Analysis, and has played a fundamental role, both because it has several deep theoretical consequences and since there have been a lot of studies and applications in various branches of Mathematics and other sciences, e.g., Subdifferential Calculus, Optimization, Operations Research, Numerical Analysis, Differential Equations, Calculus of Variations, Measure theory, Probability, Image Restoration (see, e.g., [2,3,8,11,12,16]). Some other related topics are, for instance, amenable (semi)groups, invariant and equivariant functionals, which are widely used in Probability, Statistics and Machine Learning (see, e.g.…”