Looking for an accessible explanation of Henstock–Kurzweil (gauge) integral
up vote
3
down vote
favorite
I'm not completely new to analysis, but I'm an engineer -- very applied, not very theoretical -- looking into self-studying pure mathematics. I've recently stumbled upon Henstock–Kurzweil integrals; many internet articles state that it's a very intuitive idea, but I simply can't wrap my head around its intuitive meaning as successfully as I can do it for the Riemann integral. The Wikipedia article seems to be pretty well-written, but I probably need a simpler stated approach/definition, because I'm only starting to get into all of these things.
Can someone give me their own explanation of what the Henstock-Kurzweil is, or perhaps a good resource?
real-analysis integration analysis reference-request gauge-integral
edited Nov 19 '17 at 11:09
Martin Sleziak
44.4k7115268
asked Aug 1 '11 at 14:53
Phonon
1,37021527
add a comment |
up vote
3
down vote
favorite
I'm not completely new to analysis, but I'm an engineer -- very applied, not very theoretical -- looking into self-studying pure mathematics. I've recently stumbled upon Henstock–Kurzweil integrals; many internet articles state that it's a very intuitive idea, but I simply can't wrap my head around its intuitive meaning as successfully as I can do it for the Riemann integral. The Wikipedia article seems to be pretty well-written, but I probably need a simpler stated approach/definition, because I'm only starting to get into all of these things.
Can someone give me their own explanation of what the Henstock-Kurzweil is, or perhaps a good resource?
real-analysis integration analysis reference-request gauge-integral
edited Nov 19 '17 at 11:09
Martin Sleziak
44.4k7115268
asked Aug 1 '11 at 14:53
Phonon
1,37021527
1
How about this book? amazon.com/Introduction-Gauge-Integrals-Charles-Swartz/dp/…
– Max Muller
Aug 1 '11 at 15:04
1
A Garden of Integrals has a chapter on Henstock-Kurzweil, and goes into some detail about the differences with the other integrals.
– Arturo Magidin
Aug 1 '11 at 20:01
1
I'd like to second very strongly the piece of advice given by Didier Piau about Demailly's documents. Demailly's thesis is essentially that HK-integral could be taught as a first integration theory, so around the end of high school. To prove this (admittedly bold) thesis, he wrote what could be an introduction aiming this kind of audience (this is the “light” version, www-fourier.ujf-grenoble.fr/~demailly/manuscripts/…) I think that's as easy as it gets. Even if your command of French is shaky, you should definitely take a look at it.
– PseudoNeo
Aug 1 '11 at 21:15
@PseudoNeo Thank you, though my knowledge of French is quite poor. I will definitely look into it, the diagrams alone are a great help.
– Phonon
Aug 2 '11 at 0:18
add a comment |
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I'm not completely new to analysis, but I'm an engineer -- very applied, not very theoretical -- looking into self-studying pure mathematics. I've recently stumbled upon Henstock–Kurzweil integrals; many internet articles state that it's a very intuitive idea, but I simply can't wrap my head around its intuitive meaning as successfully as I can do it for the Riemann integral. The Wikipedia article seems to be pretty well-written, but I probably need a simpler stated approach/definition, because I'm only starting to get into all of these things.
Can someone give me their own explanation of what the Henstock-Kurzweil is, or perhaps a good resource?
real-analysis integration analysis reference-request gauge-integral
edited Nov 19 '17 at 11:09
Martin Sleziak
44.4k7115268
asked Aug 1 '11 at 14:53
Phonon
1,37021527
I'm not completely new to analysis, but I'm an engineer -- very applied, not very theoretical -- looking into self-studying pure mathematics. I've recently stumbled upon Henstock–Kurzweil integrals; many internet articles state that it's a very intuitive idea, but I simply can't wrap my head around its intuitive meaning as successfully as I can do it for the Riemann integral. The Wikipedia article seems to be pretty well-written, but I probably need a simpler stated approach/definition, because I'm only starting to get into all of these things.
Can someone give me their own explanation of what the Henstock-Kurzweil is, or perhaps a good resource?
real-analysis integration analysis reference-request gauge-integral
real-analysis integration analysis reference-request gauge-integral
edited Nov 19 '17 at 11:09
Martin Sleziak
44.4k7115268
asked Aug 1 '11 at 14:53
Phonon
1,37021527
edited Nov 19 '17 at 11:09
Martin Sleziak
44.4k7115268
asked Aug 1 '11 at 14:53
Phonon
1,37021527
edited Nov 19 '17 at 11:09
Martin Sleziak
44.4k7115268
edited Nov 19 '17 at 11:09
Martin Sleziak
44.4k7115268
edited Nov 19 '17 at 11:09
Martin Sleziak
44.4k7115268
44.4k7115268
asked Aug 1 '11 at 14:53
Phonon
1,37021527
asked Aug 1 '11 at 14:53
Phonon
1,37021527
asked Aug 1 '11 at 14:53
Phonon
1,37021527
1,37021527
1
How about this book? amazon.com/Introduction-Gauge-Integrals-Charles-Swartz/dp/…
– Max Muller
Aug 1 '11 at 15:04
1
A Garden of Integrals has a chapter on Henstock-Kurzweil, and goes into some detail about the differences with the other integrals.
– Arturo Magidin
Aug 1 '11 at 20:01
1
I'd like to second very strongly the piece of advice given by Didier Piau about Demailly's documents. Demailly's thesis is essentially that HK-integral could be taught as a first integration theory, so around the end of high school. To prove this (admittedly bold) thesis, he wrote what could be an introduction aiming this kind of audience (this is the “light” version, www-fourier.ujf-grenoble.fr/~demailly/manuscripts/…) I think that's as easy as it gets. Even if your command of French is shaky, you should definitely take a look at it.
– PseudoNeo
Aug 1 '11 at 21:15
@PseudoNeo Thank you, though my knowledge of French is quite poor. I will definitely look into it, the diagrams alone are a great help.
– Phonon
Aug 2 '11 at 0:18
add a comment |
1
How about this book? amazon.com/Introduction-Gauge-Integrals-Charles-Swartz/dp/…
– Max Muller
Aug 1 '11 at 15:04
1
A Garden of Integrals has a chapter on Henstock-Kurzweil, and goes into some detail about the differences with the other integrals.
– Arturo Magidin
Aug 1 '11 at 20:01
1
I'd like to second very strongly the piece of advice given by Didier Piau about Demailly's documents. Demailly's thesis is essentially that HK-integral could be taught as a first integration theory, so around the end of high school. To prove this (admittedly bold) thesis, he wrote what could be an introduction aiming this kind of audience (this is the “light” version, www-fourier.ujf-grenoble.fr/~demailly/manuscripts/…) I think that's as easy as it gets. Even if your command of French is shaky, you should definitely take a look at it.
– PseudoNeo
Aug 1 '11 at 21:15
@PseudoNeo Thank you, though my knowledge of French is quite poor. I will definitely look into it, the diagrams alone are a great help.
– Phonon
Aug 2 '11 at 0:18
1
1
How about this book? amazon.com/Introduction-Gauge-Integrals-Charles-Swartz/dp/…
– Max Muller
Aug 1 '11 at 15:04
How about this book? amazon.com/Introduction-Gauge-Integrals-Charles-Swartz/dp/…
– Max Muller
Aug 1 '11 at 15:04
1
1
A Garden of Integrals has a chapter on Henstock-Kurzweil, and goes into some detail about the differences with the other integrals.
– Arturo Magidin
Aug 1 '11 at 20:01
A Garden of Integrals has a chapter on Henstock-Kurzweil, and goes into some detail about the differences with the other integrals.
– Arturo Magidin
Aug 1 '11 at 20:01
1
1
I'd like to second very strongly the piece of advice given by Didier Piau about Demailly's documents. Demailly's thesis is essentially that HK-integral could be taught as a first integration theory, so around the end of high school. To prove this (admittedly bold) thesis, he wrote what could be an introduction aiming this kind of audience (this is the “light” version, www-fourier.ujf-grenoble.fr/~demailly/manuscripts/…) I think that's as easy as it gets. Even if your command of French is shaky, you should definitely take a look at it.
– PseudoNeo
Aug 1 '11 at 21:15
I'd like to second very strongly the piece of advice given by Didier Piau about Demailly's documents. Demailly's thesis is essentially that HK-integral could be taught as a first integration theory, so around the end of high school. To prove this (admittedly bold) thesis, he wrote what could be an introduction aiming this kind of audience (this is the “light” version, www-fourier.ujf-grenoble.fr/~demailly/manuscripts/…) I think that's as easy as it gets. Even if your command of French is shaky, you should definitely take a look at it.
– PseudoNeo
Aug 1 '11 at 21:15
@PseudoNeo Thank you, though my knowledge of French is quite poor. I will definitely look into it, the diagrams alone are a great help.
– Phonon
Aug 2 '11 at 0:18
@PseudoNeo Thank you, though my knowledge of French is quite poor. I will definitely look into it, the diagrams alone are a great help.
– Phonon
Aug 2 '11 at 0:18
add a comment |
3 Answers
3
active
oldest
votes
up vote
5
down vote
accepted
There is a nice beginner's treatment in section 8.1 of Abbott's Understanding analysis.
Abbott's main source is Bartle's article "Return to the Riemann integral." JSTOR link, full article
Abbott also recommends The integral: an easy approach after Kurzweil and Henstock by Lee and Výborný and A modern theory of integration by Bartle for more detailed treatments.
add a comment |
up vote
4
down vote
In my opinion the first and foremost place to explore should be Eric Schechter's webpage dedicated to the so-called gauge integral (linked on the WP page you mention).
One should probably also mention the book The Integral: An Easy Approach after Kurzweil and Henstock by Lee Peng Yee and Rudolf Vyborny, and, if you happen to read French, two very accessible introductory texts due to Jean-Pierre Demailly and available as [E3] on his webpage of teaching documents (their bibliography includes Yee and Vyborny's book).
answered Aug 1 '11 at 15:06
Did
245k23215451
add a comment |
up vote
2
down vote
How about the Carus Monograph:
R. M. McLeod, Generalized Riemann Integral (Carus Mathematical Monographs) (Mathematical Association of America, 1982)
It may be out of print, so look in libraries.
answered Aug 1 '11 at 17:41
GEdgar
61.1k266167
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
There is a nice beginner's treatment in section 8.1 of Abbott's Understanding analysis.
Abbott's main source is Bartle's article "Return to the Riemann integral." JSTOR link, full article
Abbott also recommends The integral: an easy approach after Kurzweil and Henstock by Lee and Výborný and A modern theory of integration by Bartle for more detailed treatments.
add a comment |
up vote
5
down vote
accepted
There is a nice beginner's treatment in section 8.1 of Abbott's Understanding analysis.
Abbott's main source is Bartle's article "Return to the Riemann integral." JSTOR link, full article
Abbott also recommends The integral: an easy approach after Kurzweil and Henstock by Lee and Výborný and A modern theory of integration by Bartle for more detailed treatments.
add a comment |
up vote
5
down vote
accepted
up vote
5
down vote
accepted
There is a nice beginner's treatment in section 8.1 of Abbott's Understanding analysis.
Abbott's main source is Bartle's article "Return to the Riemann integral." JSTOR link, full article
Abbott also recommends The integral: an easy approach after Kurzweil and Henstock by Lee and Výborný and A modern theory of integration by Bartle for more detailed treatments.
There is a nice beginner's treatment in section 8.1 of Abbott's Understanding analysis.
Abbott's main source is Bartle's article "Return to the Riemann integral." JSTOR link, full article
Abbott also recommends The integral: an easy approach after Kurzweil and Henstock by Lee and Výborný and A modern theory of integration by Bartle for more detailed treatments.
answered Aug 1 '11 at 15:05
community wiki
Jonas Meyer
add a comment |
add a comment |
up vote
4
down vote
In my opinion the first and foremost place to explore should be Eric Schechter's webpage dedicated to the so-called gauge integral (linked on the WP page you mention).
One should probably also mention the book The Integral: An Easy Approach after Kurzweil and Henstock by Lee Peng Yee and Rudolf Vyborny, and, if you happen to read French, two very accessible introductory texts due to Jean-Pierre Demailly and available as [E3] on his webpage of teaching documents (their bibliography includes Yee and Vyborny's book).
answered Aug 1 '11 at 15:06
Did
245k23215451
add a comment |
up vote
4
down vote
In my opinion the first and foremost place to explore should be Eric Schechter's webpage dedicated to the so-called gauge integral (linked on the WP page you mention).
One should probably also mention the book The Integral: An Easy Approach after Kurzweil and Henstock by Lee Peng Yee and Rudolf Vyborny, and, if you happen to read French, two very accessible introductory texts due to Jean-Pierre Demailly and available as [E3] on his webpage of teaching documents (their bibliography includes Yee and Vyborny's book).
answered Aug 1 '11 at 15:06
Did
245k23215451
add a comment |
up vote
4
down vote
up vote
4
down vote
In my opinion the first and foremost place to explore should be Eric Schechter's webpage dedicated to the so-called gauge integral (linked on the WP page you mention).
One should probably also mention the book The Integral: An Easy Approach after Kurzweil and Henstock by Lee Peng Yee and Rudolf Vyborny, and, if you happen to read French, two very accessible introductory texts due to Jean-Pierre Demailly and available as [E3] on his webpage of teaching documents (their bibliography includes Yee and Vyborny's book).
answered Aug 1 '11 at 15:06
Did
245k23215451
In my opinion the first and foremost place to explore should be Eric Schechter's webpage dedicated to the so-called gauge integral (linked on the WP page you mention).
One should probably also mention the book The Integral: An Easy Approach after Kurzweil and Henstock by Lee Peng Yee and Rudolf Vyborny, and, if you happen to read French, two very accessible introductory texts due to Jean-Pierre Demailly and available as [E3] on his webpage of teaching documents (their bibliography includes Yee and Vyborny's book).
answered Aug 1 '11 at 15:06
Did
245k23215451
edited Aug 1 '11 at 15:18
answered Aug 1 '11 at 15:06
Did
245k23215451
answered Aug 1 '11 at 15:06
Did
245k23215451
answered Aug 1 '11 at 15:06
Did
245k23215451
245k23215451
add a comment |
add a comment |
up vote
2
down vote
How about the Carus Monograph:
R. M. McLeod, Generalized Riemann Integral (Carus Mathematical Monographs) (Mathematical Association of America, 1982)
It may be out of print, so look in libraries.
answered Aug 1 '11 at 17:41
GEdgar
61.1k266167
add a comment |
up vote
2
down vote
How about the Carus Monograph:
R. M. McLeod, Generalized Riemann Integral (Carus Mathematical Monographs) (Mathematical Association of America, 1982)
It may be out of print, so look in libraries.
answered Aug 1 '11 at 17:41
GEdgar
61.1k266167
add a comment |
up vote
2
down vote
up vote
2
down vote
How about the Carus Monograph:
R. M. McLeod, Generalized Riemann Integral (Carus Mathematical Monographs) (Mathematical Association of America, 1982)
It may be out of print, so look in libraries.
answered Aug 1 '11 at 17:41
GEdgar
61.1k266167
How about the Carus Monograph:
R. M. McLeod, Generalized Riemann Integral (Carus Mathematical Monographs) (Mathematical Association of America, 1982)
It may be out of print, so look in libraries.
answered Aug 1 '11 at 17:41
GEdgar
61.1k266167
answered Aug 1 '11 at 17:41
GEdgar
61.1k266167
answered Aug 1 '11 at 17:41
GEdgar
61.1k266167
answered Aug 1 '11 at 17:41
GEdgar
61.1k266167
61.1k266167
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f54953%2flooking-for-an-accessible-explanation-of-henstock-kurzweil-gauge-integral%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
1
How about this book? amazon.com/Introduction-Gauge-Integrals-Charles-Swartz/dp/…
– Max Muller
Aug 1 '11 at 15:04
1
A Garden of Integrals has a chapter on Henstock-Kurzweil, and goes into some detail about the differences with the other integrals.
– Arturo Magidin
Aug 1 '11 at 20:01
1
I'd like to second very strongly the piece of advice given by Didier Piau about Demailly's documents. Demailly's thesis is essentially that HK-integral could be taught as a first integration theory, so around the end of high school. To prove this (admittedly bold) thesis, he wrote what could be an introduction aiming this kind of audience (this is the “light” version, www-fourier.ujf-grenoble.fr/~demailly/manuscripts/…) I think that's as easy as it gets. Even if your command of French is shaky, you should definitely take a look at it.
– PseudoNeo
Aug 1 '11 at 21:15
@PseudoNeo Thank you, though my knowledge of French is quite poor. I will definitely look into it, the diagrams alone are a great help.
– Phonon
Aug 2 '11 at 0:18