Question

Approach to compute 3 dim volume

score 41 · Answer 1 · 2026-04-02 18:37:37

41

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Approach to compute 3 dim volume

Published on 02 Apr 2026 - 18:37

score 232 · Answer 2 · 2026-04-03 01:23:12

232

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The homogeneous sobolev space and the Fourier transform

Published on 03 Apr 2026 - 1:23

score 1k · Answer 3 · 2017-02-17 00:19:40

1k

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Can we split up any lebesgue integral into sum of integrals?

Published on 17 Feb 2017 - 0:19

score 47 · Answer 4 · 2017-02-17 01:08:30

47

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Show that$\int |f(x)−\varphi(x)|\,dx < \epsilon$, where $f$ is in $L$

Published on 17 Feb 2017 - 1:08

score 227 · Answer 5 · 2017-02-17 12:24:51

227

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Prove $f=0$ when $ \int_{A} f(x)dx=0$ for every Jordan Measurable set $A$.

Published on 17 Feb 2017 - 12:24

score 1.2k · Answer 6 · 2017-02-17 23:44:25

1.2k

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If$f_n$ a sequence of integrable functions on a set of finite measure which converge to f uniformly, then the limit and integral can be swapped.

Published on 17 Feb 2017 - 23:44

score 63 · Answer 7 · 2017-02-17 23:47:33

63

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Let $f \in L$ and $0 \le f < 1$. Show that $\lim_{n\to\infty}\int f^n~dx = 0$

Published on 17 Feb 2017 - 23:47

score 68 · Answer 8 · 2017-02-18 18:20:50

68

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The sobolev space and it's dual space

Published on 18 Feb 2017 - 18:20

score 36 · Answer 9 · 2026-04-02 18:42:53

36

Views

Volume of $E=\{ (x,y,z)\in \mathbb R^3 | x^2+y^2\le4, x^2+y^2+z^2\le 16 \}$

Published on 02 Apr 2026 - 18:42

score 66 · Answer 10 · 2017-02-18 21:48:52

66

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$\int_E \frac{y^2}{x^2}d\lambda^2(x,y)$ for $E=\{ (x,y)\in\mathbb R^2 : x\le y, xy\ge 1, y\le2 \}$

Published on 18 Feb 2017 - 21:48

score 183 · Answer 11 · 2017-02-19 00:33:27

183

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If $\psi$ is a nonnegative simple function check that $\int \psi = \sup\{\int\phi:0\le\phi\le\psi, \phi\, \text{simple and integrable}\}$

Published on 19 Feb 2017 - 0:33

score 18 · Answer 12 · 2026-03-21 02:42:58

18

Views

Spaces containing a two variable functions

Published on 21 Mar 2026 - 2:42

score 36 · Answer 13 · 2026-04-06 11:39:08

36

Views

$f_j \rightarrow f$ in $L_1$ then $\mathcal{F}(f_j) \rightarrow \mathcal{F}(f)$ in measure

Published on 06 Apr 2026 - 11:39

score 43 · Answer 14 · 2017-02-19 14:01:07

43

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$\int_{-\infty}^\infty f=\lim_{n\to\infty} \int_{-n}^nf=\lim_{n\to\infty} \int_{\{f\ge(1/n)\}}f=\lim_{n\to\infty} \int_{\{f\le n\}}f$

Published on 19 Feb 2017 - 14:01

score 1.3k · Answer 15 · 2017-02-19 14:26:35

1.3k

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Let $f$ be measurable with $f$>0 a.e. If $ \int_E f$=0 for some measurable set E, show that m(E)=0.

Published on 19 Feb 2017 - 14:26

List Question

Approach to compute 3 dim volume

The homogeneous sobolev space and the Fourier transform

Can we split up any lebesgue integral into sum of integrals?

Show that$\int |f(x)−\varphi(x)|\,dx < \epsilon$, where $f$ is in $L$

Prove $f=0$ when $ \int_{A} f(x)dx=0$ for every Jordan Measurable set $A$.

If$f_n$ a sequence of integrable functions on a set of finite measure which converge to f uniformly, then the limit and integral can be swapped.

Let $f \in L$ and $0 \le f < 1$. Show that $\lim_{n\to\infty}\int f^n~dx = 0$

The sobolev space and it's dual space

Volume of $E=\{ (x,y,z)\in \mathbb R^3 | x^2+y^2\le4, x^2+y^2+z^2\le 16 \}$

$\int_E \frac{y^2}{x^2}d\lambda^2(x,y)$ for $E=\{ (x,y)\in\mathbb R^2 : x\le y, xy\ge 1, y\le2 \}$

If $\psi$ is a nonnegative simple function check that $\int \psi = \sup\{\int\phi:0\le\phi\le\psi, \phi\, \text{simple and integrable}\}$

Spaces containing a two variable functions

$f_j \rightarrow f$ in $L_1$ then $\mathcal{F}(f_j) \rightarrow \mathcal{F}(f)$ in measure

$\int_{-\infty}^\infty f=\lim_{n\to\infty} \int_{-n}^nf=\lim_{n\to\infty} \int_{\{f\ge(1/n)\}}f=\lim_{n\to\infty} \int_{\{f\le n\}}f$

Let $f$ be measurable with $f$>0 a.e. If $ \int_E f$=0 for some measurable set E, show that m(E)=0.

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