Integration

The aim of this course is to provide a general framework for functional analysis and integration that will be useful for the theoretical and numerical study of parial differential equations. More precisely, the course consists of the following 3 parts:
1) Integration: measurable functions, Lebesgue integral, Lebesgue dominated convergence theorem, change of variables, Fubini's theorem, parameter integral, Lp space, double and triple integrals: examples.
2) Fourier analysis: Fourier transform in S, L^1 and L^2, Fourier inversion formula.
3) Hilbert analysis: projection theorem, Riesz theorem, Hilbert space, weak convergence, Sobolev spaces.

Topology of R^n (norms, compactness), vector space.