Square-integrable function

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Covers convergence theorems and integrable functions, including the Lebesgue integral and Borel-Cantelli sets.

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

Explores cylindrical coordinates, integrability, and volume calculations using examples.

Explores abstract integration of functions and the need for stronger conditions beyond continuity.

Explores embedding in function spaces, including elliptic equations, Hölder inequality, Lorentz space, and Hardy-Young inequality.

Covers various examples of function spaces and linear applications between them.

Explores negligible sets, integrable sets, and almost everywhere concept in mathematical analysis.

Introduces continuity in function spaces and the Galerkin method for solving boundary value problems.

Explores templates of (un)stable subbundles and the approximation of temporal-distance functions in 3-dimensional Anosov flows.

Covers weak derivatives, interpolation spaces, and continuity in function spaces.