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:
fr.tipeee.com/kobipy/
A comment, a like or a share are also appreciated 😉
The animations were made in Python, with the Manim module:
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:
mast.queensu.ca/~andrew/notes...
fr.wikipedia.org/wiki/Int%C3%...
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 :
• Pourquoi une autre déf...
Негізгі бет The Myth of the HORIZONTAL Lebesgue integral | Episode 3
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