Talk:Henstock–Kurzweil integral

message: 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. ).
-- 15:46, 9 Feb 2005 (UTC)
replies: text: 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)
replies: text: 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 ;-) 19:44, 11 Feb 2005 (UTC)
thread_title: Educational use

message: Probably a diagram similar to this should be added to the page.  --128.163.161.42 (talk) 10:31, 23 March 2008 (UTC)
thread_title: Diagram

message: I added a section called "Properties" which describes a few key properties of the gauge integral.  (Also I removed the paragraph from the text about the fundamental theorem of calculus and added corresponding material in this section.)  In particular, I added the 
characterization of gauge integrable functions in terms of Lebesgue integrable functions.  
It would be nice to be more explicit about the fact that the gauge integral, unlike the Riemann and Lebesgue integrals, is a "nonasbsolute integral" i.e., integrability of f does not imply 
integrability of |f|.  
Is it now time to remove the extremely vague and unhelpful statement about the gauge integral 
being "in some situations more useful" than the Lebesgue integral?  We have now called attention to several particular uses: (i) integration of all derivatives; (ii) inclusion of 
improper Riemann integrals; (iii) arguably more elementary definition.  72.152.92.55 (talk) 23:11, 23 November 2007 (UTC)
replies: text: Just added a statement on Hake's theorem. --a_dergachev (talk) 09:12, 14 February 2008 (UTC)
thread_title: A few changes

message: In Real Analysis Exchange 33(1) pp51-82, Erik Talvila has defined an extraordinarily simple integral which takes Dejoy, Henstock, Lebesgue & Reimann as special cases. The definition is: given distribution f, if there exists a continuous function F with real limit at infinity such that F' = f (distributional derivative) then define \int_{-\infty}^\infty f = F(\infty)-F(-\infty). Integrable distributions form a Banach space, and its dual is \mathcal{BV}. He then derives int by parts, a very general change of variables, convergence theorems, Holder inequality and other properties.
Just giving heads up! --Pwsnafu (talk) 03:58, 2 July 2008 (UTC)
thread_title:  distributional Denjoy integral 

message: I question the sentence:" Due to these two important mathematicians, it is now commonly known as the Henstock–Kurzweil integral." I suspect that it is a poor translation..(?). As is, this sentence clearly implies that both Henstock and Kurzweil caused the integral to be named after themselves. Its common for mathmeticians to claim a bit too much credit, but in this case I wonder if the text is correct. I suspect that the author meant "Due to the importance of their work with/on it, it is commonly known as the Henstock-Kurzweil integral."  If they did not claim priority and not lobby for a name change, would someone change the above to make clear what is being said?  Thanks173.189.73.72 (talk) 23:10, 25 January 2014 (UTC)
replies: text: Heh. Good one! Someone corrected it; it now says "Due to these two important contributions..." 67.198.37.16 (talk) 20:12, 20 September 2020 (UTC)
thread_title:  Question of cause/meaning 

message: I use the idea of the gauge integral as a bridge from Riemann to Lebesgue integration in Sect.1 "Introduction" of my course Functions of a real variable. There you can also find my explanation, why use it as just a bridge, not instead of Lebesgue integral. Boris Tsirelson (talk) 16:11, 11 March 2016 (UTC)
thread_title:  To use or not to use it when teaching 

message: Edit March 20: The weird definition of Lebesgue integration got me, the article is fine.  Yodo9000 (talk) 11:02, 14 March 2022 (UTC)
thread_title:  ... calculating that integral gives the same result by all three formulations