> Using Riemann Integration > Adding up rectangles that

Lehesgue integration is super duper thin rectangles to you stupid. They're literally just oriented differently.

>not using Barnett triple integrals

super duper thin 4 dimensional hyper rectangles are too complex for brainlets

Actually it divides the interval of integration into small partitions, minimums, maximums, infima and suprema

Lebesgue integration just calls every integral the supremum of a "simple function" and puts these non-decreasing simple functions into an infinite amount of sets via the characteristic functions

At least I think so. Taking my first reals/measure class now.

Let's be honest here, integration is for brainlets. Differentiation is the endeavor of the enlightened. Fractional Sobolev spaces on [math]L^p_{ul}[/math] is where the patrician sets their sights.

File: 1502700914429-r9k.jpg (72KB, 632x620px) Image search: [Google]

72KB, 632x620px

>integration
>needing limits
>no euclidean geometry
>no method of exhaustion

When will brainlets learn?

>>9171246
Lebesgue integration is the same as Riemann integration if you make enough assumptions.

The point is that if you don't make such assumptions you get a much more general object that behaves much the same way

File: 1396118652169.jpg (7KB, 321x306px) Image search: [Google]

7KB, 321x306px

>>9171268
>puts these non-decreasing simple functions into an infinite amount of sets via the characteristic functions

>>9171243
Sounds like someone needs to watch Wildberger's new series on algebraic calculus (signed area lectures) where he does away with this rectangle nonsense.

>>9171739
> Not just using rectangles + a few scaled quarter-circles

>>9171243
funky sum baby

>>9171748
>not an uncountable number of non-measurable sets to cover your area of integration to btfo lebesgue cucks