Question

Give an example of unbounded continuous function that is Lebesgue integrable on $\mathbb{R}$?

score 590 · Answer 1 · 2017-03-01 04:53:29

590

Views

Give an example of unbounded continuous function that is Lebesgue integrable on $\mathbb{R}$?

Published on 01 Mar 2017 - 4:53

score 123 · Answer 2 · 2026-04-09 04:45:19

123

Views

repeated integration of lebesgue integrable function

Published on 09 Apr 2026 - 4:45

score 72 · Answer 3 · 2017-03-01 22:47:17

72

Views

Unclear on justification for Lebesgue integral identity

Published on 01 Mar 2017 - 22:47

score 1.1k · Answer 4 · 2026-04-08 20:27:05

1.1k

Views

How to justify Dirac delta in integral kernels?

Published on 08 Apr 2026 - 20:27

score 97 · Answer 5 · 2017-03-02 13:46:52

97

Views

Solve integral $\int \int \int_A \frac{dxdydz}{(x+y+1)^2}$ where $A=\{(x,y,z):0<x<1, 0<x+y<1, 0<z(x+y+1)<1\}$

Published on 02 Mar 2017 - 13:46

score 28 · Answer 6 · 2017-03-02 15:01:37

28

Views

Find volume of $A=\{(x,y,z): 4x^2+y^2<4,x>0,x^2>z>0\}$. Review solution.

Published on 02 Mar 2017 - 15:01

score 77 · Answer 7 · 2017-03-04 11:53:21

77

Views

Riemann and Lebesgue integrals as sums of infimums

Published on 04 Mar 2017 - 11:53

score 122 · Answer 8 · 2017-03-06 01:28:55

122

Views

Continuous function defined on a Lebesgue integrable function?

Published on 06 Mar 2017 - 1:28

score 112 · Answer 9 · 2017-03-06 14:41:19

112

Views

Problem with integral$\int_A\frac{x+y}{(1+(x+y)^2)^2}dxdy$

Published on 06 Mar 2017 - 14:41

score 37 · Answer 10 · 2026-04-06 14:36:23

37

Views

An example such that $||x \hat{f}||_{L^2(\mathbb{R}^n)} = \infty$

Published on 06 Apr 2026 - 14:36

score 69 · Answer 11 · 2017-03-07 08:15:34

69

Views

Typo on proof of Riemann Lebesgue proofwiki(?)

Published on 07 Mar 2017 - 8:15

score 30 · Answer 12 · 2017-03-08 08:59:21

30

Views

Element of $L^p(\mathbb{R}^d)$

Published on 08 Mar 2017 - 8:59

score 51 · Answer 13 · 2026-04-06 16:19:35

51

Views

$\int_{\mathbb{R}} |x|^{\frac{1}{2}} |f(x)|^2 dx < \infty$ and $\int_{\mathbb{R}} |\xi|^{\frac{1}{2}} |\hat{f}(\xi)|^2 d\xi = \infty$

Published on 06 Apr 2026 - 16:19

score 950 · Answer 14 · 2017-03-08 21:48:50

950

Views

Showing that $1/\sqrt{x}$ on $(0,1)$ is in $L^1$

Published on 08 Mar 2017 - 21:48

score 42 · Answer 15 · 2017-03-09 01:38:53

42

Views

If $f:A \to \Bbb R$ is bounded and $c\in A$, then $f$ is continuous at $c$ iff $w(f;c) = 0$

Published on 09 Mar 2017 - 1:38

List Question

Give an example of unbounded continuous function that is Lebesgue integrable on $\mathbb{R}$?

repeated integration of lebesgue integrable function

Unclear on justification for Lebesgue integral identity

How to justify Dirac delta in integral kernels?

Solve integral $\int \int \int_A \frac{dxdydz}{(x+y+1)^2}$ where $A=\{(x,y,z):0<x<1, 0<x+y<1, 0<z(x+y+1)<1\}$

Find volume of $A=\{(x,y,z): 4x^2+y^2<4,x>0,x^2>z>0\}$. Review solution.

Riemann and Lebesgue integrals as sums of infimums

Continuous function defined on a Lebesgue integrable function?

Problem with integral$\int_A\frac{x+y}{(1+(x+y)^2)^2}dxdy$

An example such that $||x \hat{f}||_{L^2(\mathbb{R}^n)} = \infty$

Typo on proof of Riemann Lebesgue proofwiki(?)

Element of $L^p(\mathbb{R}^d)$

$\int_{\mathbb{R}} |x|^{\frac{1}{2}} |f(x)|^2 dx < \infty$ and $\int_{\mathbb{R}} |\xi|^{\frac{1}{2}} |\hat{f}(\xi)|^2 d\xi = \infty$

Showing that $1/\sqrt{x}$ on $(0,1)$ is in $L^1$

If $f:A \to \Bbb R$ is bounded and $c\in A$, then $f$ is continuous at $c$ iff $w(f;c) = 0$

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