Bourgain's Theorem: Frechet Embedding and Lemma

Delves into the completeness of Lp spaces and the density of function classes in L².

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.