Question

Showing that $f \in R_\alpha[a,b]$ and $\lim_{n\rightarrow \infty}\int_a^b f d\alpha_n = \int_a^b f d\alpha $

score 114 · Answer 1 · 2026-03-25 14:35:52

114

Views

Showing that $f \in R_\alpha[a,b]$ and $\lim_{n\rightarrow \infty}\int_a^b f d\alpha_n = \int_a^b f d\alpha $

Published on 25 Mar 2026 - 14:35

score 31 · Answer 2 · 2019-04-09 17:36:16

31

Views

Lower and upper sums of a bounded function

Published on 09 Apr 2019 - 17:36

score 183 · Answer 3 · 2026-03-26 04:36:24

183

Views

Question about Riemann integrability: do we need to specify that all Riemann sums converge to the same number in the definition?

Published on 26 Mar 2026 - 4:36

score 563 · Answer 4 · 2026-03-25 14:35:53

563

Views

Show that if $f \in R_\alpha$,and g increasing and continuous then $ f(g(x)) \in R_{\alpha(g(x))}$

Published on 25 Mar 2026 - 14:35

score 278 · Answer 5 · 2026-03-26 19:18:30

278

Views

Volume of a tilted cylinder

Published on 26 Mar 2026 - 19:18

score 42 · Answer 6 · 2026-03-26 04:31:26

42

Views

Calculating upper Riemann sum. Is it sufficient to only consider "simple" partitions

Published on 26 Mar 2026 - 4:31

score 117 · Answer 7 · 2019-04-11 19:07:10

117

Views

Two definitions for Riemann integrability of $f:[a,b]\rightarrow X$, where $X$ is a Banach space.

Published on 11 Apr 2019 - 19:07

score 63 · Answer 8 · 2026-03-25 23:37:32

63

Views

How to prove that a function is of bounded outside variation?

Published on 25 Mar 2026 - 23:37

score 90 · Answer 9 · 2019-04-12 15:12:39

90

Views

Is "Cumulative CDF" a studied topic?

Published on 12 Apr 2019 - 15:12

score 176 · Answer 10 · 2026-03-25 17:21:49

176

Views

Integral inequality $\int_{0}^{1}|f(x)|dx \leq \int_{0}^{1}x|f'(x)|dx$

Published on 25 Mar 2026 - 17:21

score 80 · Answer 11 · 2019-04-14 18:43:38

80

Views

If $f(x)=\int_a^x f(t)dt$, is $f(x)=0$?

Published on 14 Apr 2019 - 18:43

score 206 · Answer 12 · 2019-04-15 01:40:42

206

Views

Problem with Definition of Riemann Integrable Function

Published on 15 Apr 2019 - 1:40

score 187 · Answer 13 · 2026-03-25 18:59:06

187

Views

Integral inequality $\int_{0}^{1}\left ( \frac{f(x)}{x} \right )^2dx \leq 4\int_{0}^{1}(f'(x))^2dx$

Published on 25 Mar 2026 - 18:59

score 69 · Answer 14 · 2019-04-18 23:29:43

69

Views

How to find $f(x)$ if $\int_0^{x^2} (1+t)f'(t)dt=x^4$ and $\int_0^1 f(t)dt=3 $

Published on 18 Apr 2019 - 23:29

score 1.9k · Answer 15 · 2019-04-20 13:18:54

1.9k

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Examples of Lebesgue-integrable, but not Riemann-integrable functions

Published on 20 Apr 2019 - 13:18

List Question

Showing that $f \in R_\alpha[a,b]$ and $\lim_{n\rightarrow \infty}\int_a^b f d\alpha_n = \int_a^b f d\alpha $

Lower and upper sums of a bounded function

Question about Riemann integrability: do we need to specify that all Riemann sums converge to the same number in the definition?

Show that if $f \in R_\alpha$,and g increasing and continuous then $ f(g(x)) \in R_{\alpha(g(x))}$

Volume of a tilted cylinder

Calculating upper Riemann sum. Is it sufficient to only consider "simple" partitions

Two definitions for Riemann integrability of $f:[a,b]\rightarrow X$, where $X$ is a Banach space.

How to prove that a function is of bounded outside variation?

Is "Cumulative CDF" a studied topic?

Integral inequality $\int_{0}^{1}|f(x)|dx \leq \int_{0}^{1}x|f'(x)|dx$

If $f(x)=\int_a^x f(t)dt$, is $f(x)=0$?

Problem with Definition of Riemann Integrable Function

Integral inequality $\int_{0}^{1}\left ( \frac{f(x)}{x} \right )^2dx \leq 4\int_{0}^{1}(f'(x))^2dx$

How to find $f(x)$ if $\int_0^{x^2} (1+t)f'(t)dt=x^4$ and $\int_0^1 f(t)dt=3 $

Examples of Lebesgue-integrable, but not Riemann-integrable functions

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