List questions from stieltjes-integral

Published on 10 Dec 2019 - 8:14

112

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Under what conditions does this "two dimensional Riemann-Stieltjes integral" exist?

Published on 19 Mar 2026 - 16:59

65

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Monotone convergence for Stieltjes integral

Published on 21 Jan 2020 - 9:56

147

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Compute the Riemann-Stieltjes integral $\int_{-1}^1 \cos x\ \mathsf dg(x)$ without reduction.

Published on 23 Jan 2020 - 4:12

41

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Compute the Riemann-Stieltjes integral

Published on 23 Jan 2020 - 21:00

76

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Stieltjes integral and dominated convergence

Published on 28 Jan 2020 - 15:18

81

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Show that f is Riemann-Stieltjes Integrable. Is my solution correct?

Published on 03 Feb 2020 - 2:19

148

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Computing probability as a Lebesgue-Stieltjes integral

Published on 20 Feb 2020 - 23:49

106

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If $f\in R(\alpha)$ and $C\in\mathbb{R}$, then $Cf\in R(\alpha)$ and $\int_a^b Cf\operatorname{d}\alpha=C\int_a^b f\operatorname{d}\alpha.$

Published on 23 Feb 2026 - 4:58

106

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Are increasing functions Riemann-Stieltjes integrable?

Published on 05 Mar 2020 - 19:44

55

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Proof verification: Possibly false argument in the proof of $\int_{I}g(x)dF(u)=\int_{I}g(u)F'(u)du$ (Riemann-Stieltjes)

Published on 29 Mar 2020 - 20:24

79

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(Proof) $g\in BV[a,b]$ and $f\in\mathcal{R}_g[a,b]$ and $f$ bounded $\Rightarrow 1/f\in\mathcal{R}_g[a,b]$

Published on 31 Mar 2020 - 1:32

38

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Characterization of all functions which are Riemann-Stieltjes-integrable with respect to $g$

Published on 08 Apr 2020 - 18:10

79

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Evaluating $\int x f(x)\ \mathrm{d}f(x)$

Published on 25 Apr 2020 - 14:10

475

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Prove by definition that $ \int_a^b fdf = {f^2(b)-f^2(a) \over{2}}$ when $f$ is continuous

Published on 30 Apr 2020 - 4:06

List Question

Two dimensional Riemann-Stieltjes integral.

Under what conditions does this "two dimensional Riemann-Stieltjes integral" exist?

Monotone convergence for Stieltjes integral

Compute the Riemann-Stieltjes integral $\int_{-1}^1 \cos x\ \mathsf dg(x)$ without reduction.

Compute the Riemann-Stieltjes integral

Stieltjes integral and dominated convergence

Show that f is Riemann-Stieltjes Integrable. Is my solution correct?

Computing probability as a Lebesgue-Stieltjes integral

If $f\in R(\alpha)$ and $C\in\mathbb{R}$, then $Cf\in R(\alpha)$ and $\int_a^b Cf\operatorname{d}\alpha=C\int_a^b f\operatorname{d}\alpha.$

Are increasing functions Riemann-Stieltjes integrable?

Proof verification: Possibly false argument in the proof of $\int_{I}g(x)dF(u)=\int_{I}g(u)F'(u)du$ (Riemann-Stieltjes)

(Proof) $g\in BV[a,b]$ and $f\in\mathcal{R}_g[a,b]$ and $f$ bounded $\Rightarrow 1/f\in\mathcal{R}_g[a,b]$

Characterization of all functions which are Riemann-Stieltjes-integrable with respect to $g$

Evaluating $\int x f(x)\ \mathrm{d}f(x)$

Prove by definition that $ \int_a^b fdf = {f^2(b)-f^2(a) \over{2}}$ when $f$ is continuous

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