1. Know Fubini theorem, use it to determine some integrales "doubles and triples".
2. Lebesgue measure in Rⁿ.
3. Determine a function that we know its Fourier transform.
4. Compute the convolution product.
5. Know the relations between the convergence in Lp and the simple convergence(construction of a sequence ).
6. Apply the Hilbert technique in L2.
7. Technique of density of a measure. Function absolutely continuous.
8. Duality injection and compacity between the spaces in Lp or the construction of a measure et the Theorem of Daniel.
Measures products, Measure of Lebesgue in Rⁿ. Theorems of Tonelli and Fubini. Convolution in L1, properties of the Fourier transform in L1.
Analytical study of the spaces L2,orthogonal system et orthonormal. Inversion of the Fourier transform in L1 and L2, Fourier-Plancherel, L2(T).
Space Lp, Theorem of Radon – Nykodim, measure absolutely continuous, singular measure.
Duality injection and compacity between the spaces Lp or the construction of a measure and the Theorem of Daniel.