Descriptif

Prerequisite: MAA202
MAA301 proposes an introduction to the modern theory of integration. The first part of this course is focused on the construction of the Lebesgue integral, an extension of the Riemann integral to a class of functions much larger than the set of Riemann-integrable functions. With the Lebesgue theory of integration, passing to the limit in integrals of sequences of functions is an easy task which rests on the  verification of a few essentially optimal assumptions. The end of the course offers an introduction to Lebesgue spaces and the Fourier transform, with applications to physics. The abstract theory of integration discussed at the beginning of this course provides the setting used in probability theory and stochastic analysis.