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Concentration InequalitiesCovers concentration inequalities and sampling methods for estimating unknown distributions, with a focus on population infection rates.
Embedding in Function SpacesExplores embedding in function spaces, including elliptic equations, Hölder inequality, Lorentz space, and Hardy-Young inequality.
Properties of Complete SpacesCovers the properties of complete spaces, including completeness, expectations, embeddings, subsets, norms, Holder's inequality, and uniform integrability.
Convex Sets and FunctionsIntroduces convex sets and functions, discussing minimizers, optimality conditions, and characterizations, along with examples and key inequalities.