Question

Show that $\int fd\mu>0$ iff $\mu(\{x\in X: f(x)>0\})>0$.

score 191 · Answer 1 · 2023-03-19 19:21:28

191

Views

Show that $\int fd\mu>0$ iff $\mu(\{x\in X: f(x)>0\})>0$.

Published on 19 Mar 2023 - 19:21

score 29 · Answer 2 · 2026-04-09 22:51:08

29

Views

References a ideas behind weight functions

Published on 09 Apr 2026 - 22:51

score 30 · Answer 3 · 2026-04-09 23:27:06

30

Views

Principle value vs Lebsgue integrability

Published on 09 Apr 2026 - 23:27

score 75 · Answer 4 · 2026-03-26 16:07:11

75

Views

Fast numerical integration of an integral of the form $\int_{[0,\:1)^d}\left|f\right|\:{\rm d}\lambda^{\otimes d}$

Published on 26 Mar 2026 - 16:07

score 46 · Answer 5 · 2023-03-22 08:30:58

46

Views

If $f$ is Lebesgue integrable, is $f^2$ also Lebesgue integrable?

Published on 22 Mar 2023 - 8:30

score 28 · Answer 6 · 2026-04-11 15:33:05

28

Views

Expressing surface area in terms of line integral

Published on 11 Apr 2026 - 15:33

score 410 · Answer 7 · 2026-04-09 11:50:49

410

Views

Wasserstein distance inequality

Published on 09 Apr 2026 - 11:50

score 32 · Answer 8 · 2026-04-11 12:41:38

32

Views

Inclusion of Lebesgue spaces on finite measure space

Published on 11 Apr 2026 - 12:41

score 39 · Answer 9 · 2026-04-09 06:06:26

39

Views

How do I show the differentiation under integral sign when Leibnitz rule does not work?

Published on 09 Apr 2026 - 6:06

score 83 · Answer 10 · 2023-03-27 01:51:14

83

Views

Prove that $\displaystyle{\lim_{k \to \infty}} k^{n-1} \phi(k) f(kx) \neq 0$

Published on 27 Mar 2023 - 1:51

score 245 · Answer 11 · 2026-04-12 01:44:05

245

Views

Proof of Riemann-Lebesgue lemma. What is the dominated function in this case?

Published on 12 Apr 2026 - 1:44

score 105 · Answer 12 · 2023-03-28 07:18:21

105

Views

If $f'\notin L^1([a,b])$ then $f$ is not a bounded variation on $[a,b]$

Published on 28 Mar 2023 - 7:18

score 79 · Answer 13 · 2026-03-28 06:48:15

79

Views

Using $(e^{ik\cdot x})$ as an orthonormal basis for $L^2(\mathbb{R}^d;\mathbb{C})$ to define trace.

Published on 28 Mar 2026 - 6:48

score 27 · Answer 14 · 2026-04-10 23:27:49

27

Views

Given a $\sigma$-algebra $\mathcal{S}$, is $\mu:\mathcal{S}\to 0$ a valid measure?

Published on 10 Apr 2026 - 23:27

score 153 · Answer 15 · 2026-04-12 00:35:22

153

Views

Validity of a proof of the Fisher Information Data Processing inequality, $I(f(X)) \le I(X)$.

Published on 12 Apr 2026 - 0:35

List Question

Show that $\int fd\mu>0$ iff $\mu(\{x\in X: f(x)>0\})>0$.

References a ideas behind weight functions

Principle value vs Lebsgue integrability

Fast numerical integration of an integral of the form $\int_{[0,\:1)^d}\left|f\right|\:{\rm d}\lambda^{\otimes d}$

If $f$ is Lebesgue integrable, is $f^2$ also Lebesgue integrable?

Expressing surface area in terms of line integral

Wasserstein distance inequality

Inclusion of Lebesgue spaces on finite measure space

How do I show the differentiation under integral sign when Leibnitz rule does not work?

Prove that $\displaystyle{\lim_{k \to \infty}} k^{n-1} \phi(k) f(kx) \neq 0$

Proof of Riemann-Lebesgue lemma. What is the dominated function in this case?

If $f'\notin L^1([a,b])$ then $f$ is not a bounded variation on $[a,b]$

Using $(e^{ik\cdot x})$ as an orthonormal basis for $L^2(\mathbb{R}^d;\mathbb{C})$ to define trace.

Given a $\sigma$-algebra $\mathcal{S}$, is $\mu:\mathcal{S}\to 0$ a valid measure?

Validity of a proof of the Fisher Information Data Processing inequality, $I(f(X)) \le I(X)$.

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