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Banach–Alaoglu theorem
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Measure Spaces: Integration and Inequalities
Covers measure spaces, integration, Radon-Nikodym property, and inequalities like Jensen, Hölder, and Minkowski.
Existence of y: Proofs and EDO Resolution
Covers the proof of the existence of y and the resolution of EDOs with practical examples.
Normed Spaces & Reflexivity
Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.
Functional Spaces: Linear Applications
Explores functional spaces, linear applications, sublinear functionals, and the Hahn-Banach theorem.
Functional Analysis I: Foundations and Applications
Covers the foundations of modern analysis, introductory functional analysis, and applications in MAB111.
Duality: Lagrangian and Dual Problem
Covers Lagrangian, dual function, dual problem, weak duality, and optimality.
Sobolev Spaces and Continuous Embeddings
Covers Sobolev spaces, continuous embeddings, weak convergence, and Poincare inequalities.
Functional Analysis I
Covers sublinear functionals, linear functionals extension, and Hahn-Banach theorem.
Sobolev Spaces in Higher Dimensions
Explores Sobolev spaces in higher dimensions, discussing derivatives, properties, and challenges with continuity.
Interpolation Spaces
Explores interpolation spaces between Banach spaces and real interpolation spaces.