Question

What if we replace step functions by a different class of functions in the definition of Riemann integral?

score 101 · Answer 1 · 2017-12-12 02:32:10

101

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What if we replace step functions by a different class of functions in the definition of Riemann integral?

Published on 12 Dec 2017 - 2:32

score 185 · Answer 2 · 2017-12-23 20:25:20

185

Views

Show that the following function has a gauge-integral and calculate its value.

Published on 23 Dec 2017 - 20:25

score 11.7k · Answer 3 · 2011-03-21 05:51:05

11.7k

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Why are gauge integrals not more popular?

Published on 21 Mar 2011 - 5:51

score 965 · Answer 4 · 2011-08-01 14:53:05

965

Views

Looking for an accessible explanation of Henstock–Kurzweil (gauge) integral

Published on 01 Aug 2011 - 14:53

score 1.2k · Answer 5 · 2011-10-24 06:23:52

1.2k

Views

Integrability: Neither improper Riemann nor Lebesgue but Henstock-Kurzweil

Published on 24 Oct 2011 - 6:23

score 185 · Answer 6 · 2013-01-28 18:49:48

185

Views

Proof that if $f,g,h:[a,b]\to \mathbb{R}$ with $h\le f,g$ and $f,g,h$ are gauge integrable then so is $\min(f,g)$

Published on 28 Jan 2013 - 18:49

score 875 · Answer 7 · 2013-01-30 10:09:05

875

Views

Mistake in Bartle's proof of Hake's Theorem?

Published on 30 Jan 2013 - 10:09

score 159 · Answer 8 · 2013-01-31 13:34:06

159

Views

Proof of $f=0$ a.e. in $[a,b]$ then $f$ is gauge integrable and $\int_a^bf=0$

Published on 31 Jan 2013 - 13:34

score 71 · Answer 9 · 2021-06-29 18:59:33

71

Views

Does the law of large numbers hold with the Henstock–Kurzweil integral?

Published on 29 Jun 2021 - 18:59

score 532 · Answer 10 · 2021-09-07 18:22:12

532

Views

Is every "almost everywhere derivative" Henstock–Kurzweil integrable?

Published on 07 Sep 2021 - 18:22

score 53 · Answer 11 · 2021-09-26 18:00:50

53

Views

Can the LCT and MCT for Lebesgue integrable functions be viewed as a lattice completeness result?

Published on 26 Sep 2021 - 18:00

score 223 · Answer 12 · 2022-03-10 14:19:01

223

Views

Is there a constructive presentation of the Henstock-Kurzweil integral?

Published on 10 Mar 2022 - 14:19

score 162 · Answer 13 · 2022-04-07 03:52:41

162

Views

If $f(x)$ is Henstock-Kurzweil integrable on $[a,b]$, then is $f(x)\mathrm{e}^{\mathrm{i}x}$ also Henstock-Kurzweil integrable on $[a,b]$?

Published on 07 Apr 2022 - 3:52

score 53 · Answer 14 · 2022-09-28 17:58:20

53

Views

Some questions concerning the construction of the line integral in $\mathbb{C}$

Published on 28 Sep 2022 - 17:58

score 269 · Answer 15 · 2022-10-02 08:38:44

269

Views

What makes Cousin's theorem remarkable?

Published on 02 Oct 2022 - 8:38

List Question

What if we replace step functions by a different class of functions in the definition of Riemann integral?

Show that the following function has a gauge-integral and calculate its value.

Why are gauge integrals not more popular?

Looking for an accessible explanation of Henstock–Kurzweil (gauge) integral

Integrability: Neither improper Riemann nor Lebesgue but Henstock-Kurzweil

Proof that if $f,g,h:[a,b]\to \mathbb{R}$ with $h\le f,g$ and $f,g,h$ are gauge integrable then so is $\min(f,g)$

Mistake in Bartle's proof of Hake's Theorem?

Proof of $f=0$ a.e. in $[a,b]$ then $f$ is gauge integrable and $\int_a^bf=0$

Does the law of large numbers hold with the Henstock–Kurzweil integral?

Is every "almost everywhere derivative" Henstock–Kurzweil integrable?

Can the LCT and MCT for Lebesgue integrable functions be viewed as a lattice completeness result?

Is there a constructive presentation of the Henstock-Kurzweil integral?

If $f(x)$ is Henstock-Kurzweil integrable on $[a,b]$, then is $f(x)\mathrm{e}^{\mathrm{i}x}$ also Henstock-Kurzweil integrable on $[a,b]$?

Some questions concerning the construction of the line integral in $\mathbb{C}$

What makes Cousin's theorem remarkable?

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