The Interpretation of Henstock Integral

Question

If riemann integral has interpretation as the area under function, then what the interpretation of henstock integral? I always think bout it but don't get it

score 1 · Answer 1 · answered Nov 11 '15 at 16:23

1

The Henstock integral is also interpreted as "area under a function". The difference is that certain functions that are not Riemann integrable are Henstock integrable. For example, the characteristic function of the rationals on $[0,1]$.

answered Nov 11 '15 at 16:23

GEdgar

111,679

Can I get the journal bout that statement? – Albert Parulian Nov 11 '15 at 16:36
@Albert Parulian: Better yet, just look at the Wikipedia article on the Henstock integral. – Dave L. Renfro Nov 11 '15 at 16:44
Link https://en.wikipedia.org/wiki/Henstock–Kurzweil_integral for Henstock integral. – GEdgar Nov 11 '15 at 16:56
Hm okay, but why the characteristic function of the rationals on that interval are not Riemann integrable? – Albert Parulian Nov 12 '15 at 07:11
1

Not Riemann integrable: all upper sums are 1, all lower sums are 0. – GEdgar Nov 12 '15 at 14:46

The Interpretation of Henstock Integral

1 Answers1