Duality Principle: Radon Measures and Homeomorphisms

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

Explores interpolation spaces in Banach spaces, emphasizing real continuous interpolation spaces and the K-method.

Explains the definition of Sobolew spaces and their main properties, focusing on weak denivelre.

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Covers the Meyers-Serrin theorem in analysis, discussing the conditions for functions in different spaces.

Covers the compact-open topology, defining maps between spaces and discussing continuous maps and preimages in topology.

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

Introduces recollements, showing how to build new spaces by assembling and gluing them together.

Covers the proof and identification of isomorphisms in the Seifert van Kampen theorem.