"Every Lebesgue Integrable function is Henstock-Kurzweil integrable"
Is this really true? Should there be a condition that the function should
have contable number of areas of discontinuity?
For example, the following function:
w(x) = 1 if rational, -1 if irrational on [0,1].
Lebegue(w) = -1
What about HK? If the partition contains only rational values?
Or am I missing something in the HK definition?

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Clarification of Question by mikhailscientist-ga on 20 Aug 2004 05:41 PDT

Should there be a condition for HK that the function should
have a countable number of points of discontinuity (or something like that)?