Question

function vanishing at infinity and integrability

score 412 · Answer 1 · 2018-12-12 12:35:39

412

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function vanishing at infinity and integrability

Published on 12 Dec 2018 - 12:35

score 4.1k · Answer 2 · 2018-12-12 19:46:20

4.1k

Views

Showing $f(x) = \frac{1}{\sqrt x}$ is Lebesgue integrable on $(0,1]$

Published on 12 Dec 2018 - 19:46

score 131 · Answer 3 · 2026-03-25 03:22:12

131

Views

Let $T(f)(y)=\int_0^\infty K(x,y)\cdot f(x)dx$, $\,$ show $\,$ $\Vert T(f) \Vert _p \le C\cdot \Vert f \Vert _p$

Published on 25 Mar 2026 - 3:22

score 167 · Answer 4 · 2018-12-14 13:20:31

167

Views

Equality of integrals with non-negative functions

Published on 14 Dec 2018 - 13:20

score 69 · Answer 5 · 2018-12-14 22:09:32

69

Views

Let $f_n:[1,\infty) \rightarrow \mathbb{R}$ be defined by $f_n(x)=\frac{1}{x}\chi_{[n,\infty)}(x)$. Does $\int f_n \to \int f$?

Published on 14 Dec 2018 - 22:09

score 123 · Answer 6 · 2018-12-15 11:29:52

123

Views

Show that Lebesgue integration is continuous

Published on 15 Dec 2018 - 11:29

score 68 · Answer 7 · 2018-12-15 14:30:18

68

Views

Average (determine with Lebesgue integral/measure)

Published on 15 Dec 2018 - 14:30

score 79 · Answer 8 · 2018-12-15 23:00:55

79

Views

Let $f:(0;\infty)\times (0;\infty) \rightarrow \Bbb R$ be a Lebesgue measurable function, is $T_f(y)=\int_0^{+\infty} f(x,y) \, dy$ measurable?

Published on 15 Dec 2018 - 23:00

score 122 · Answer 9 · 2018-12-16 12:05:50

122

Views

Matrix with $\det(A)=1$ in Lebesgue integral

Published on 16 Dec 2018 - 12:05

score 60 · Answer 10 · 2018-12-16 13:43:58

60

Views

$f \in L_1([0,1],m)$ such that $\int_0^1 f \sin (n^2x) \ dm= 1$

Published on 16 Dec 2018 - 13:43

score 353 · Answer 11 · 2018-12-16 22:00:57

353

Views

Operator norm on Lebesgue integrable functions

Published on 16 Dec 2018 - 22:00

score 212 · Answer 12 · 2026-03-28 00:48:03

212

Views

Inequality for the $L^2$ norm of a derivative in a Dirichlet problem

Published on 28 Mar 2026 - 0:48

score 172 · Answer 13 · 2026-03-25 12:15:03

172

Views

Riemann integrable function implies discontinuous on a Borel set?

Published on 25 Mar 2026 - 12:15

score 2.8k · Answer 14 · 2018-12-19 07:57:41

2.8k

Views

L^2 convergence and pointwise convergence

Published on 19 Dec 2018 - 7:57

score 68 · Answer 15 · 2018-12-19 09:32:42

68

Views

$\int_{[-1,1]}\int_{[-1,1]}\frac{xy}{(x^2+y^2)^2}d\lambda(x) d\lambda(y)= \int_{[-1,1]}\int_{[-1,1]}\frac{xy}{(x^2+y^2)^2}d\lambda(y) d\lambda(x)$

Published on 19 Dec 2018 - 9:32

List Question

function vanishing at infinity and integrability

Showing $f(x) = \frac{1}{\sqrt x}$ is Lebesgue integrable on $(0,1]$

Let $T(f)(y)=\int_0^\infty K(x,y)\cdot f(x)dx$, $\,$ show $\,$ $\Vert T(f) \Vert _p \le C\cdot \Vert f \Vert _p$

Equality of integrals with non-negative functions

Let $f_n:[1,\infty) \rightarrow \mathbb{R}$ be defined by $f_n(x)=\frac{1}{x}\chi_{[n,\infty)}(x)$. Does $\int f_n \to \int f$?

Show that Lebesgue integration is continuous

Average (determine with Lebesgue integral/measure)

Let $f:(0;\infty)\times (0;\infty) \rightarrow \Bbb R$ be a Lebesgue measurable function, is $T_f(y)=\int_0^{+\infty} f(x,y) \, dy$ measurable?

Matrix with $\det(A)=1$ in Lebesgue integral

$f \in L_1([0,1],m)$ such that $\int_0^1 f \sin (n^2x) \ dm= 1$

Operator norm on Lebesgue integrable functions

Inequality for the $L^2$ norm of a derivative in a Dirichlet problem

Riemann integrable function implies discontinuous on a Borel set?

L^2 convergence and pointwise convergence

$\int_{[-1,1]}\int_{[-1,1]}\frac{xy}{(x^2+y^2)^2}d\lambda(x) d\lambda(y)= \int_{[-1,1]}\int_{[-1,1]}\frac{xy}{(x^2+y^2)^2}d\lambda(y) d\lambda(x)$

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