[FOM] Category and Measure
joeshipman@aol.com
joeshipman at aol.com
Tue Sep 18 21:21:03 EDT 2007
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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