Lebesgue integral Updated +Created
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 +Created
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 +Created
Main motivation: Lebesgue integral.
The key idea, is that we can't define a measure for the power set of R. Rather, we must select a large measurable subset, and the Borel sigma algebra is a good choice that matches intuitions.
Riemann integral Updated +Created
The easy and less generic integral. The harder one is the Lebesgue integral.