ECTS: 3 ECTS-point.
Prerequisites: one should have previously followed Analysis 1 and 2 on MAT1, and Differentiable curves and manifolds on MAT3.
Content: Integration of positive measurable functions; the monotone and dominated convergence theorems. The Lebesgue measure on Rn and its invariance. Product-measure, Tonelli and Fubini theorems. Hölder and Minkowski inequalities; Lebesgue-spaces and their completeness. Approximation by smooth functions. Convolution and approximation of identity. Fourier series, Riesz-Fischer theorem; orthogonal expansions in Hilbert spaces. The Fourier transform and the inversion theorem; Plancherel's identity.
Exam: oral examination, with intern censorship.
Each lecture is organized as follows:
One should read the indicated material in advance, and try to solve the given exercises beforehand.