Do you still remember the difference between Rieman and Lebesgue

With the Riemann integral you had upper and lower sums and they had to converge to the same value

I don't really remember the Lebesgue integral but I recall there was something wonky with finitely-valued functions

there is a difference?

Well whenever both are defined, they take the same values so...

>>8619831
in math, "almost every time" is important

>>8619566
Lebesgue integration is far more useful in mathematical physics, so yes.

>>8619566
i remember the difference in how they're formulated
i remember some things are riemann integrable but not lebesgue and vise versa

>>8619853
examples?

>>8620296
Measurements in quantum mechanics expressed via integrals w.r.t. projection-valued measures. Also, of course the various probability measures that can be involved.

The only way to properly express feynman integrals require integration w.r.t. all sorts of measures. (The measure dependent upon what the action is)

>>8620335
what is a feynman integral?

>>8620341
Path integrals / Functional Integrals

For instance for the simple action [math]S\left[ x \right] = \int\limits_0^t {\operatorname{ds} {{\left| {\frac{{\operatorname{dx} }}{{\operatorname{ds} }}} \right|}^2}} [/math], the measure, [math]{Dx}[/math] ,in the functional integral [math]\int {Dx\exp \left( { - S\left[ x \right]} \right)} [/math] needs to be a Wiener style measure.

>>8620359
>Path integrals / Functional Integrals
gotcha, never heard the name feynman integral before :O)

>>8620359
I'll not have anyone measuring my wiener, thank you.

File: 93e.png (25KB, 165x115px) Image search: [Google]

25KB, 165x115px

>>8620359
>Wiener style measure

File: 1474152886091.jpg (29KB, 480x480px) Image search: [Google]

29KB, 480x480px

>>8620359
>Wiener style measure

>>8620675
>>8620680
>>8620683
https://www.encyclopediaofmath.org/index.php/Wiener_measure

>>8620700
>https://www.encyclopediaofmath.org/index.php/Wiener_measure
Don't have to go to your wikipedia link to know its NINE INCHES BITCH