[FOM] Category and Measure

[joeshipman@aol.com]

The Henstock/Kurzweil/Denjoy/Perron integral, which extends the 
Lebesgue integral, is described here:

http://en.wikipedia.org/wiki/Henstock-Kurzweil_integral

It satisfies a very strong version of the F.T. of C. -- every function 
which is a derivative of some other function is integrable.

An example of a function which is Henstock integrable but not Lebesgue 
integrable is

f(x) = (1/x) sin(1/(x^3))

-- for this function, you can calculate the integral except over 
[-epsilon, +epsilon] and let epsilon go to 0 and you get a consistent 
answer.

-- JS

****
-----Original Message-----
From: Timothy Y. Chow <tchow at alum.mit.edu>

---from a foundational point of view, what other theories of
integration are there, that arguably have some advantages over the
Lebesgue theory?
****

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