Le MYTHE De l'Intégrale De Lebesgue HORIZONTALE ? | Épisode 3

In this third episode of our series on integration, we tackle the myth of the horizontal Lebesgue integral. Many photos on the Internet seem to suggest that the Lebesgue integral is horizontal, in the sense that it is visualized using horizontal rectangles. Where does it come from? A misunderstanding of the definition or, on the contrary, is there something deeper behind these images? During our journey to answer these questions, we will encounter new concepts (the layer-cake decomposition or the f star function...)! As usual, the emphasis is on visualizations, as well as the transmission of the mathematical "feeling" that lies behind the sometimes off-putting formalism. For those who would like to support me: https://fr.tipeee.com/kobipy/ A comment, a like or a share are also appreciated 😉 The animations were made in Python, with the Manim module: https://www.manim.community/ The background music is: Piano Music by: Bensound.com/free-music-for-videos License code: 3I3OM2PI2LQIVVCH ⏲ ​​Timestamps: 00:00 – Introduction 00:32 - What is the horizontal integral? 04:28 - Myth or reality? 07:37: Conclusion 09:42: Outro Bibliography: https://mast.queensu.ca/~andrew/notes... https://fr.wikipedia.org/wiki/Int%C3%... https://perso.univ-rennes1.fr/jean-ch... Books : Goudon: Integration - Lebesgue integral and introduction to functional analysis Briend: Small treatise on integration: Riemann, Lebesgue and Kurweil-Henstock Lieb & Loss: AMS Analysis Other videos from the channel that may interest you: ◆ The Power of the LEBESGUE Integral | Épisode 2 :    • En quoi l'Intégrale de LEBESGUE est-elle S...