Talk:Henstock-Kurzweil integral

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This was in the text of the article:

This topic is somewhat esoteric: most mathematical departments do not teach it even for graduate students, and specialists in this field are numbered. Consider reading first Riemann integral (the oldest and simplest definition) or Lebesgue integral (the most common).

I believe Uffish added that remark.

I disagree with this Point Of View. The Denjoy-Perron-Henstock-Kurzweil integral is part of the first year course in Mathematics and also Physics at the Université catholique de Louvain, Louvain-la-Neuve, Belgium. The course is given by Jean Mawhin (J. Mawhin, Analyse : fondements, techniques, évolution. De Boeck Université, Bruxelles, 1992. ISBN 2-8041-1670-0). --Eruionnyron 15:46, 9 Feb 2005 (UTC)

Well, that still doesn't make it taught at most departments. In the past proponents of this approach have written things here designed to 'promote' this approach. Not surprisingly there was a negative reaction. Charles Matthews 16:35, 9 Feb 2005 (UTC)

Thanks for the explanation. It sometimes seems to me that mathematicians in any field are numbered and that all of mathematics is viewed as esoteric ;-) Eruionnyron 19:44, 11 Feb 2005 (UTC)

It would be nice to see how this definition relates to Lebesgue integration beyond the statement that it "in some situations is more useful than the Lebesgue integral." It is easy to see that all Riemann integrable functions are Henstock-Kurzweil integrable, but does Henstock-Kurzweil itegrability imply Lebesgue integrability, or vice versa? Althai 05:17, 31 January 2007 (UTC)

If I recall correctly, at the external site, it is stated that Lebesgue integrability implies gauge integrability. Indeed, the example at the start of the article gives a function that is not Lebesgue integrable but is gauge integrable. If somebody confirms this, then maybe further emphasis can be added to article on these points DRLB 15:08, 31 January 2007 (UTC)