Measurement and integration

Acquire the fundamentals of measure theory and integration.

This EU will address the following points:

- General theory of measure: measurable spaces, measurable applications, and measured spaces.

- General theory of integration: integrals of step functions, positive measurable functions, and then real or complex functions. Monotone and dominated convergence theorems. Continuity and differentiability of integrals depending on a parameter.

-Examples of measures: image measures and the transfer theorem, counting measures on N, Lebesgue measures on R ⁿ

The L1 and L2 analysis courses, in particular:

-HAX302X Analysis 3, Topology of R ⁿ and Functions of Several Variables

- HAX403X Analysis 4, Function sequences, entire series, Fourier

 

Recommended prerequisites: L2 maths

Hourly volumes:

            CM: 36

            TD: 36

            TP: -

            Land: -