[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:


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 

-- 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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