Real world applications of the Lebesgue integral by 
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01In "practice" it is likely "useless", because the functions that it can integrate that Riemann can't are just too funky to appear in practice :-)
Its value is much more indirect and subtle, as in "it serves as a solid basis of quantum mechanics" due to the definition of Hilbert spaces.
Sample usages:
- quantum computing startup Atom Computing uses them to hold dozens of individual atoms midair separately, to later entangle their nuclei
Optical Tweezers Experiment by Alexis Bishop
. Source. Setup on a optical table. He drags a 1 micron ball of polystyrene immersed in water around with the laser. You look through the microscope and move the stage. Brownian motion is also clearly visible when the laster is not holding the ball. Equivalence between Lagrangian and Hamiltonian formalisms by Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01 Symmetric and public-key cryptography by Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-07-01 +Created 1970-01-01www.youtube.com/playlist?list=PLVV0r6CmEsFzCodipONmNiROhYCUWyz_U interview with Walter Murch by Web of Stories. He worked on sound design for all The Godfather films, and tells some interesting details about it. He's just super nice in general otherwise. E.g.:
- www.youtube.com/watch?v=w4OK8__gfGo talks about the sound design for the restaurant scene in The Godfather Part II (1974)
1959 by Voice of America.
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