Measurement and integration

Acquire the basics of measurement theory and integration.

This UE will cover the following points:

- General measurement theory: measurable spaces, measurable applications and measured spaces.

- General theory of integration: integrals of stepped functions, positive measurable functions and real or complex functions. Monotone and dominated convergence theorems. Continuity and derivability of integrals dependent on a parameter.

- Examples of measures: image measures and the transfer theorem, the counting measure on N, the Lebesgue measure on ^Rn

Analysis courses in L1 and L2, in particular :

- HAX302X Analysis 3, topology of ^Rn and functions of several variables

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

Recommended prerequisites: L2 maths

Hourly volumes :

            CM: 36

            TD : 36

            TP: -

            Land: -