Measure Theory and Wavelets (O)

3 ch (3C) · Undergraduate

Brief review of Riemann integration. Algebras of sets, outer measure, measure, measurable sets, measurable functions, the Lebesgue integral, properties of the Lebesgue integral, abstract measure spaces, integrals and derivatives, sequences of integrals, Fubini's theorem. Properties of Fourier transforms, multiresolution analysis, Daubechies wavelets.