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Problem 3. Page 240. Barry Simon. (Associated Lebesgue-Stieltjes measure )

score 101 · Answer 1 · 2018-11-25 20:57:06

101

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Problem 3. Page 240. Barry Simon. (Associated Lebesgue-Stieltjes measure )

Published on 25 Nov 2018 - 20:57

score 1.1k · Answer 2 · 2026-03-23 02:41:11

1.1k

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Continuity of Lebesgue Stieltjes integral

Published on 23 Mar 2026 - 2:41

score 1k · Answer 3 · 2026-03-25 08:12:40

1k

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Riesz representation theorem for $C([0,1])$

Published on 25 Mar 2026 - 8:12

score 671 · Answer 4 · 2019-01-07 20:58:57

671

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why is the Lebesgue-Stieltjes integral well-defined?

Published on 07 Jan 2019 - 20:58

score 87 · Answer 5 · 2019-02-06 15:21:16

87

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Asymptotics of integrals with respect to asymptotically equivalent distribution functions

Published on 06 Feb 2019 - 15:21

score 149 · Answer 6 · 2019-02-14 14:59:50

149

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Riemann-Stieltjes integrable and Right-continouos function

Published on 14 Feb 2019 - 14:59

score 87 · Answer 7 · 2019-02-23 19:31:43

87

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Extensions of Riemann-Stieltjes without continuity problems

Published on 23 Feb 2019 - 19:31

score 293 · Answer 8 · 2019-03-11 18:38:53

293

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Riemann-Stieltjes integral with respect to a product of functions.

Published on 11 Mar 2019 - 18:38

score 107 · Answer 9 · 2026-03-25 07:44:35

107

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What is the usual definition of the spectral measure for a nonnegative self-adjoint operator on a Hilbert space?

Published on 25 Mar 2026 - 7:44

score 77 · Answer 10 · 2019-04-02 19:48:43

77

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If $f$ is nondecreasing and $h$ is of bounded variation with $|h(t)-h(s)|≤C\sqrt{f(t)-f(s)}$, then $\int|X||{\rm d}h|≤C\sqrt{\int|X|^2\:{\rm d}f}$

Published on 02 Apr 2019 - 19:48

score 101 · Answer 11 · 2019-04-06 19:45:07

101

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Show that $\sum_{{i = 1}}^{n} f(i) = \lfloor n \rfloor f(n)- \int_{1}^{n}f'(x)\lfloor x\rfloor\, dx$

Published on 06 Apr 2019 - 19:45

score 388 · Answer 12 · 2019-04-07 18:26:23

388

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If $f \in BV[0,2\pi], f(0)= f(2\pi)$ Show that $\int_0^{2\pi}f(x)\sin(nx)dx$ exist for each $n$ natural.

Published on 07 Apr 2019 - 18:26

score 113 · Answer 13 · 2019-04-07 22:39:41

113

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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 07 Apr 2019 - 22:39

score 648 · Answer 14 · 2019-04-10 12:43:33

648

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Change of variables - Lebesgue-Stieltjes integral

Published on 10 Apr 2019 - 12:43

score 562 · Answer 15 · 2019-04-11 02:59:52

562

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

Published on 11 Apr 2019 - 2:59

List Question

Problem 3. Page 240. Barry Simon. (Associated Lebesgue-Stieltjes measure )

Continuity of Lebesgue Stieltjes integral

Riesz representation theorem for $C([0,1])$

why is the Lebesgue-Stieltjes integral well-defined?

Asymptotics of integrals with respect to asymptotically equivalent distribution functions

Riemann-Stieltjes integrable and Right-continouos function

Extensions of Riemann-Stieltjes without continuity problems

Riemann-Stieltjes integral with respect to a product of functions.

What is the usual definition of the spectral measure for a nonnegative self-adjoint operator on a Hilbert space?

If $f$ is nondecreasing and $h$ is of bounded variation with $|h(t)-h(s)|≤C\sqrt{f(t)-f(s)}$, then $\int|X||{\rm d}h|≤C\sqrt{\int|X|^2\:{\rm d}f}$

Show that $\sum_{{i = 1}}^{n} f(i) = \lfloor n \rfloor f(n)- \int_{1}^{n}f'(x)\lfloor x\rfloor\, dx$

If $f \in BV[0,2\pi], f(0)= f(2\pi)$ Show that $\int_0^{2\pi}f(x)\sin(nx)dx$ exist for each $n$ natural.

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 $

Change of variables - Lebesgue-Stieltjes integral

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

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