Question

Accuracy in Riemann-Stieltjes integrals

score 44 · Answer 1 · 2021-04-13 19:32:00

44

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Accuracy in Riemann-Stieltjes integrals

Published on 13 Apr 2021 - 19:32

score 157 · Answer 2 · 2026-04-01 11:29:13

157

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Prove that $L(f,[a, b])=\lim _{n \rightarrow \infty} L\left(f, P_{n},[a, b]\right)$, where $f$ is a bounded function

Published on 01 Apr 2026 - 11:29

score 57 · Answer 3 · 2021-04-18 17:45:36

57

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Using Riemann Integral determine the limit

Published on 18 Apr 2021 - 17:45

score 40 · Answer 4 · 2021-04-19 06:25:48

40

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$\lim_{n \rightarrow \infty} \prod_{k=1} ^ n \left( 1+ \frac{1}{n}f\left(\frac{k}{n}\right) \right)= e^{\int_0 ^1 f(x)dx} $

Published on 19 Apr 2021 - 6:25

score 144 · Answer 5 · 2026-03-26 13:00:45

144

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Stieltjes integral of product of two functions is zero

Published on 26 Mar 2026 - 13:00

score 123 · Answer 6 · 2021-04-19 19:32:50

123

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Is there always a Riemann integrable $g$ for a Lebesgue integrable $f$ so that $f = g$ a.e.

Published on 19 Apr 2021 - 19:32

score 177 · Answer 7 · 2021-04-21 07:33:43

177

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Is $f(x) =x^{-2}$ Riemann-Integrable on [0,2] if we set f(0) = 0?

Published on 21 Apr 2021 - 7:33

score 223 · Answer 8 · 2021-04-21 18:32:05

223

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$\lim_{n \to \infty} \sqrt[k]{\prod_{k=1}^n \left(1+ \frac{k}{n}\right)}$

Published on 21 Apr 2021 - 18:32

score 604 · Answer 9 · 2021-04-22 14:50:58

604

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Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$

Published on 22 Apr 2021 - 14:50

score 31 · Answer 10 · 2021-04-23 10:57:36

31

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Approximate a Riemann integrable function by a Riemann integrable simple function

Published on 23 Apr 2021 - 10:57

score 107 · Answer 11 · 2021-04-23 13:13:40

107

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$\sup\{\frac{1}{f(x)}|x\in[a,b]\} = \frac{1}{\inf\{f(x)|x\in[a,b]\}}$: but is it?

Published on 23 Apr 2021 - 13:13

score 95 · Answer 12 · 2026-04-01 11:29:49

95

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find the limit of the sum $\sum_{k=n}^{2n-1}\frac{1}{2k+1}$

Published on 01 Apr 2026 - 11:29

score 150 · Answer 13 · 2021-04-24 08:15:13

150

Views

Reasoning about integrable positive function

Published on 24 Apr 2021 - 8:15

score 98 · Answer 14 · 2021-04-25 03:32:13

98

Views

Proving a lemma of integrability

Published on 25 Apr 2021 - 3:32

score 531 · Answer 15 · 2021-04-25 06:37:35

531

Views

A question about Riemann Integral, the function is not integrable, but the limit of Riemann sum exists

Published on 25 Apr 2021 - 6:37

List Question

Accuracy in Riemann-Stieltjes integrals

Prove that $L(f,[a, b])=\lim _{n \rightarrow \infty} L\left(f, P_{n},[a, b]\right)$, where $f$ is a bounded function

Using Riemann Integral determine the limit

$\lim_{n \rightarrow \infty} \prod_{k=1} ^ n \left( 1+ \frac{1}{n}f\left(\frac{k}{n}\right) \right)= e^{\int_0 ^1 f(x)dx} $

Stieltjes integral of product of two functions is zero

Is there always a Riemann integrable $g$ for a Lebesgue integrable $f$ so that $f = g$ a.e.

Is $f(x) =x^{-2}$ Riemann-Integrable on [0,2] if we set f(0) = 0?

$\lim_{n \to \infty} \sqrt[k]{\prod_{k=1}^n \left(1+ \frac{k}{n}\right)}$

Finding $\lim_{n\to\infty}\int_0^{\frac{1}{2^n}}(1+\cos(x))^n\,dx$

Approximate a Riemann integrable function by a Riemann integrable simple function

$\sup\{\frac{1}{f(x)}|x\in[a,b]\} = \frac{1}{\inf\{f(x)|x\in[a,b]\}}$: but is it?

find the limit of the sum $\sum_{k=n}^{2n-1}\frac{1}{2k+1}$

Reasoning about integrable positive function

Proving a lemma of integrability

A question about Riemann Integral, the function is not integrable, but the limit of Riemann sum exists

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