Question

Find a necessary and sufficient condition for the integrabiity of a function

score 67 · Answer 1 · 2026-03-30 13:43:39

67

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Find a necessary and sufficient condition for the integrabiity of a function

Published on 30 Mar 2026 - 13:43

score 31 · Answer 2 · 2019-08-06 09:04:28

31

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The point-wise most probable outcome of a measurable function is measurable

Published on 06 Aug 2019 - 9:04

score 94 · Answer 3 · 2026-03-30 13:40:42

94

Views

About the Lebesgue integrability of $f$

Published on 30 Mar 2026 - 13:40

score 116 · Answer 4 · 2026-03-25 09:36:20

116

Views

Find $\lim_{n\rightarrow \infty}\int_0^\infty \frac{x^{n-2}\cos(n\pi x)}{1+x^n} dx$

Published on 25 Mar 2026 - 9:36

score 1.9k · Answer 5 · 2019-08-09 04:53:54

1.9k

Views

Given $m\in[0,1]$, can we find a dense subset of $[0,1]$ whose Lebesgue measure is exactly $m$?

Published on 09 Aug 2019 - 4:53

score 119 · Answer 6 · 2019-08-11 13:08:08

119

Views

A set of Lebesgue measure zero

Published on 11 Aug 2019 - 13:08

score 172 · Answer 7 · 2019-08-11 14:08:05

172

Views

Existence of a positive measure square in a positive measure set in $\mathbb{R}^2$.

Published on 11 Aug 2019 - 14:08

score 34 · Answer 8 · 2026-03-27 13:48:31

34

Views

$f_n(x) = \chi_{B_{\frac{1}{n}}(x_0)}/\lambda^N({B_{\frac{1}{n}}(x_0)}) \longrightarrow \delta_{x_0}$ in $\mathscr{D'}(\Omega)$

Published on 27 Mar 2026 - 13:48

score 33 · Answer 9 · 2019-08-12 11:28:48

33

Views

Sufficient condition on integrator that Riemann-Stieltjes integrable function on $[0,1]$ is Lebesgue integrable.

Published on 12 Aug 2019 - 11:28

score 34 · Answer 10 · 2019-08-13 06:49:45

34

Views

Hypotheses on integrator that Riemann-Stieltjes integrable function on $[0,1]$ is Lebesgue integrable on $[0,1]$.

Published on 13 Aug 2019 - 6:49

score 127 · Answer 11 · 2019-08-14 03:07:09

127

Views

Show this function is $\sigma$-additive

Published on 14 Aug 2019 - 3:07

score 1.3k · Answer 12 · 2019-08-15 13:51:33

1.3k

Views

Intuition on Dominating Measures and Absolute Continuity

Published on 15 Aug 2019 - 13:51

score 87 · Answer 13 · 2019-08-15 14:59:50

87

Views

Image measure of Lebesgue measure under $u(x)=|x|$

Published on 15 Aug 2019 - 14:59

score 91 · Answer 14 · 2026-03-30 15:18:01

91

Views

Cubes under the graph of $x^2$

Published on 30 Mar 2026 - 15:18

score 923 · Answer 15 · 2019-08-16 12:51:44

923

Views

Unbounded open and connected set with finite Lebesgue measure

Published on 16 Aug 2019 - 12:51

List Question

Find a necessary and sufficient condition for the integrabiity of a function

The point-wise most probable outcome of a measurable function is measurable

About the Lebesgue integrability of $f$

Find $\lim_{n\rightarrow \infty}\int_0^\infty \frac{x^{n-2}\cos(n\pi x)}{1+x^n} dx$

Given $m\in[0,1]$, can we find a dense subset of $[0,1]$ whose Lebesgue measure is exactly $m$?

A set of Lebesgue measure zero

Existence of a positive measure square in a positive measure set in $\mathbb{R}^2$.

$f_n(x) = \chi_{B_{\frac{1}{n}}(x_0)}/\lambda^N({B_{\frac{1}{n}}(x_0)}) \longrightarrow \delta_{x_0}$ in $\mathscr{D'}(\Omega)$

Sufficient condition on integrator that Riemann-Stieltjes integrable function on $[0,1]$ is Lebesgue integrable.

Hypotheses on integrator that Riemann-Stieltjes integrable function on $[0,1]$ is Lebesgue integrable on $[0,1]$.

Show this function is $\sigma$-additive

Intuition on Dominating Measures and Absolute Continuity

Image measure of Lebesgue measure under $u(x)=|x|$

Cubes under the graph of $x^2$

Unbounded open and connected set with finite Lebesgue measure

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