Lebesgue integration
It’s getting to be too much; everywhere I look, I see the Lebesgue measure/integral being used. Even though most applications are accompanied by ‘oh don’t worry about the details, just imagine you’re dealing with the Riemann integral— 95% of the time, you’ll only be dealing with nice cases’, I still feel like I’m missing out on something crucial.
I was digging through my stuff last night, looking for something to read right before going to bed, when I came across two sources on Lebesgue integration/measure theory: one, a tutorial by Rich Bass (the link is to a collection of notes he wrote) on measure theory and Lebesgue integration which I printed at least a year ago, and never got around to reading, and the other, the first chapter of a book on the general theory of integration, which I’m sure will give me more than enough detail. So now I can rectify my situation as regard Lebesgue theory.
Although, I just got “Lysergically yours” over interlibrary loan, so I might be spending all my time with that.
Possibly relevant posts:
- Real Analysis (11/1/2006)
- Stochastic Integration (11/15/2006)
- Lebesgue integration (8/27/2005)
Where can I find graphical depictions of the Lebesgue Integral with
some examples.
Maybe my entry on the motivation behind Lebesgue integration might help. Mostly, I don’t think anyone integrates anything with Lebesgue theory directly except for simple and close-to-being-simple functions. Instead, they rely on the fact that Riemann integrable functions are Lebesgue integrable and the two integrals are equal… so I can’t point you to good examples. Or a better graphic than in that entry
I also got very frustrated with the way this lebesgue integral is taught. I heard the same thing like you over and over . Things like “when a function is continuous on a closed interval both the Riemmann integral and the lebesgue integral are the same” .
The professor I have had never told us why and where lebesgue integral is useful in real life applications.
I keep on asking myself,if this integral is the same as Riemmann Integral in most of the cases,so why should we bother studying it?
I went through google and got this site,from which for the first time i learn that to build the lebesgue integral we deal with the range of the function,while the riemmann integral deals with partitionning the domain of the function. This is something new I’m learning now ,although I took this class before.
see this link : http://pirate.shu.edu/~wachsmut/ira/integ/lebes.html
I am also frustrated.
Why should I read over 10 chapters in my integration book and never see one good example. I am at chapter 5 and I am asking myself: Have I understood what I am reading and the answer is: NO !!!
I was studying engineering physics but I suppose the math teachers thinks it too easy…grrr…I will attend the class when I am ready…maybe after 2 years