Lebesgue integral Updated 2025-07-16
"More complex and general" integral. Matches the Riemann integral for "simple functions", but also works for some "funkier" functions that Riemann does not work for.
Ciro Santilli sometimes wonders how much someone can gain from learning this besides the beauty of mathematics, since we can hand-wave a Lebesgue integral on almost anything that is of practical use. The beauty is good reason enough though.
Lp space Updated 2025-07-16
Integrable functions to the power , usually and in this text assumed under the Lebesgue integral because: Lebesgue integral of is complete but Riemann isn't
Measure theory Updated 2025-07-16
Main motivation: Lebesgue integral.
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Riemann integral Updated 2025-07-16
The easy and less generic integral. The harder one is the Lebesgue integral.