![](/assets/images/picto-drapeau-france-3a76576a5d60a512053b4612ab58dae5.png)
4. Measurement theory and integration
The calculation of surface areas, i.e. the measurement of simple subsets of the plane, is as old as agriculture itself, and thus goes back to the most archaic mathematics. The parts of the plane whose areas are easiest to calculate are polygons, which can be written as a disjoint union (at the sides) of triangles and the sum of the areas of these triangles. When more complicated surfaces need to be measured, it's natural to enclose them between two "inner" and "outer" polygons whose area difference is small enough. This simple geometrical idea forms the basis of measurement theory, as developed by H. Lebesgue and his followers from 1901 onwards. We need to assign a "measure" (length, area, volume, etc.)
Exclusive to subscribers. 97% yet to be discovered!
You do not have access to this resource.
Click here to request your free trial access!
Already subscribed? Log in!
![](/assets/images/logo-eti-286623ed91fa802ce039246e516e5852.png)
The Ultimate Scientific and Technical Reference
This article is included in
Mathematics
This offer includes:
Knowledge Base
Updated and enriched with articles validated by our scientific committees
Services
A set of exclusive tools to complement the resources
Practical Path
Operational and didactic, to guarantee the acquisition of transversal skills
Doc & Quiz
Interactive articles with quizzes, for constructive reading
Measurement theory and integration