Real world applications of the Lebesgue integral
ID: real-world-applications-of-the-lebesgue-integral
In "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.
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