Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.
Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.
Covers the properties of complete spaces, including completeness, expectations, embeddings, subsets, norms, Holder's inequality, and uniform integrability.
Covers continuous functions with compact support, density, and approximation, focusing on the heat equation.
Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.
