Question

Example of $0\leq f\leq g$ and $E$ non measurable set s.t. $\int\limits_E f>\int\limits_E g$

score 42 · Answer 1 · 2018-06-03 07:48:48

42

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Example of $0\leq f\leq g$ and $E$ non measurable set s.t. $\int\limits_E f>\int\limits_E g$

Published on 03 Jun 2018 - 7:48

score 138 · Answer 2 · 2018-06-04 01:59:09

138

Views

showing that $\lim_{n \to \infty} \int_{\mathbb R} \frac{\sin^n(x)}{x^2} \, dx= 0$

Published on 04 Jun 2018 - 1:59

score 75 · Answer 3 · 2026-03-22 15:56:14

75

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$f \in L^1(\mathbb{R})$ and $\lim_{|x| \to +\infty} f(x) = 0$ implies $\lim_{|x| \to +\infty} \int_{\mathbb{R}} f(x-y) d\mu(y) = 0$

Published on 22 Mar 2026 - 15:56

score 245 · Answer 4 · 2018-06-05 05:22:41

245

Views

Baby Rudin Exercise 11.10 - measure theory

Published on 05 Jun 2018 - 5:22

score 157 · Answer 5 · 2026-03-25 06:10:38

157

Views

Lebesgue dominated convergence with a principal value integral

Published on 25 Mar 2026 - 6:10

score 53 · Answer 6 · 2018-06-05 11:29:44

53

Views

Integral over k-dimensional vector

Published on 05 Jun 2018 - 11:29

score 99 · Answer 7 · 2018-06-05 12:35:36

99

Views

Integrability of $\frac{x \log(x)}{(1+x)^{2}}$ on $(1, \infty)$

Published on 05 Jun 2018 - 12:35

score 313 · Answer 8 · 2018-06-05 22:29:02

313

Views

Theorem similar to dominated convergence theorem

Published on 05 Jun 2018 - 22:29

score 61 · Answer 9 · 2018-06-07 07:39:17

61

Views

Find $x(t): \int_0^1 f(t)\,\mathrm dt = 0$ and $\int_0^1 x(t)f(t)\,\mathrm dt = 0$?

Published on 07 Jun 2018 - 7:39

score 237 · Answer 10 · 2018-06-07 19:48:03

237

Views

Integrability of the sum of integrable and non-intergable functions

Published on 07 Jun 2018 - 19:48

score 55 · Answer 11 · 2026-03-25 21:50:03

55

Views

Is there an example of a function that is $L^{p_2}$ but not $L^{p_1}$ and not $L^{p_3}$?

Published on 25 Mar 2026 - 21:50

score 204 · Answer 12 · 2018-06-10 04:48:50

204

Views

Length of a partition being equal to the length of the interval

Published on 10 Jun 2018 - 4:48

score 174 · Answer 13 · 2018-06-11 14:27:39

174

Views

If $fg_n$ converges in $L^p$ for all $f\in L^p$, then $g_n$ converges in $L^\infty$.

Published on 11 Jun 2018 - 14:27

score 48 · Answer 14 · 2018-06-11 21:06:20

48

Views

$ \varphi(x_1, \dots , x_n) = (c_1x_1, \dots, c_nx_n)$. Then, $\mu(\varphi(A)) = |c_1\dots c_n|\mu(A)$, where $\mu$ is the Lebesgue measure

Published on 11 Jun 2018 - 21:06

score 49 · Answer 15 · 2018-06-12 19:26:27

49

Views

If $|\partial f / \partial x | \leq g (y)$ for some $g $ show$ \frac {d}{dx} \int f dx = \int \partial f / \partial x dy $

Published on 12 Jun 2018 - 19:26

List Question

Example of $0\leq f\leq g$ and $E$ non measurable set s.t. $\int\limits_E f>\int\limits_E g$

showing that $\lim_{n \to \infty} \int_{\mathbb R} \frac{\sin^n(x)}{x^2} \, dx= 0$

$f \in L^1(\mathbb{R})$ and $\lim_{|x| \to +\infty} f(x) = 0$ implies $\lim_{|x| \to +\infty} \int_{\mathbb{R}} f(x-y) d\mu(y) = 0$

Baby Rudin Exercise 11.10 - measure theory

Lebesgue dominated convergence with a principal value integral

Integral over k-dimensional vector

Integrability of $\frac{x \log(x)}{(1+x)^{2}}$ on $(1, \infty)$

Theorem similar to dominated convergence theorem

Find $x(t): \int_0^1 f(t)\,\mathrm dt = 0$ and $\int_0^1 x(t)f(t)\,\mathrm dt = 0$?

Integrability of the sum of integrable and non-intergable functions

Is there an example of a function that is $L^{p_2}$ but not $L^{p_1}$ and not $L^{p_3}$?

Length of a partition being equal to the length of the interval

If $fg_n$ converges in $L^p$ for all $f\in L^p$, then $g_n$ converges in $L^\infty$.

$ \varphi(x_1, \dots , x_n) = (c_1x_1, \dots, c_nx_n)$. Then, $\mu(\varphi(A)) = |c_1\dots c_n|\mu(A)$, where $\mu$ is the Lebesgue measure

If $|\partial f / \partial x | \leq g (y)$ for some $g $ show$ \frac {d}{dx} \int f dx = \int \partial f / \partial x dy $

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