Question

$\int_{\mathbb{R}}f(x)e^{-ixz}d\mu_x$ analytic for $f\in L_1$

score 274 · Answer 1 · 2014-11-21 19:26:28

274

Views

$\int_{\mathbb{R}}f(x)e^{-ixz}d\mu_x$ analytic for $f\in L_1$

Published on 21 Nov 2014 - 19:26

score 190 · Answer 2 · 2026-03-25 23:13:12

190

Views

If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?

Published on 25 Mar 2026 - 23:13

score 50 · Answer 3 · 2014-11-23 12:11:20

50

Views

Absolute continuity as a condition for $F[f^{(k)}](\lambda)=(i\lambda)^k F[f](\lambda)$

Published on 23 Nov 2014 - 12:11

score 293 · Answer 4 · 2014-11-24 12:24:30

293

Views

Lebesgue point and integration

Published on 24 Nov 2014 - 12:24

score 160 · Answer 5 · 2026-04-01 13:31:16

160

Views

For which $s$ is the function $(||x||^{s-2}x_i)^2$ integrable on the unit ball of $\mathbb R^n$?

Published on 01 Apr 2026 - 13:31

score 450 · Answer 6 · 2014-11-25 10:53:18

450

Views

Fourier transform inversion formula for $f\in L_1(\mathbb{R}^n)$ and Dini condition

Published on 25 Nov 2014 - 10:53

score 1.3k · Answer 7 · 2014-11-25 11:29:27

1.3k

Views

Uniform convergence and integrability

Published on 25 Nov 2014 - 11:29

score 85 · Answer 8 · 2014-11-25 17:55:17

85

Views

$ \int_{\mathbb{R}^n} f^p dx$ for $p>0$ and measurable $f$

Published on 25 Nov 2014 - 17:55

score 79 · Answer 9 · 2014-11-25 19:38:40

79

Views

Measurability of $f:X\times Y\to\mathbb{K}$ and $f(-,y):X\to\mathbb{K}$

Published on 25 Nov 2014 - 19:38

score 287 · Answer 10 · 2014-11-25 22:13:31

287

Views

How is Riemann–Stieltjes Integration insufficient for developing modern probability theory?

Published on 25 Nov 2014 - 22:13

score 5.7k · Answer 11 · 2014-11-26 01:45:49

5.7k

Views

$f \in L^1$, but $f \not\in L^p$ for all $p > 1$

Published on 26 Nov 2014 - 1:45

score 156 · Answer 12 · 2026-04-01 14:57:45

156

Views

Convergence in $L^p$, Cauchy in $L^\infty$

Published on 01 Apr 2026 - 14:57

score 66 · Answer 13 · 2026-03-30 05:30:11

66

Views

Lebesgue integration of $f(x)=\frac{1}{x}$ where $x\in[0,3]$

Published on 30 Mar 2026 - 5:30

score 140 · Answer 14 · 2014-11-26 16:02:20

140

Views

example of a sequence $f_n$, $n=1,2...$ of integrable functions converging to $f$ s.t limit of integral of $f_n$ does not exist

Published on 26 Nov 2014 - 16:02

score 133 · Answer 15 · 2014-11-27 05:04:36

133

Views

Prove $\lim_{n \rightarrow \infty} n \cdot \lambda(\{ f > n \}) = 0$. Where $\lambda$ is the lebesgue measure.

Published on 27 Nov 2014 - 5:04

List Question

$\int_{\mathbb{R}}f(x)e^{-ixz}d\mu_x$ analytic for $f\in L_1$

If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?

Absolute continuity as a condition for $F[f^{(k)}](\lambda)=(i\lambda)^k F[f](\lambda)$

Lebesgue point and integration

For which $s$ is the function $(||x||^{s-2}x_i)^2$ integrable on the unit ball of $\mathbb R^n$?

Fourier transform inversion formula for $f\in L_1(\mathbb{R}^n)$ and Dini condition

Uniform convergence and integrability

$ \int_{\mathbb{R}^n} f^p dx$ for $p>0$ and measurable $f$

Measurability of $f:X\times Y\to\mathbb{K}$ and $f(-,y):X\to\mathbb{K}$

How is Riemann–Stieltjes Integration insufficient for developing modern probability theory?

$f \in L^1$, but $f \not\in L^p$ for all $p > 1$

Convergence in $L^p$, Cauchy in $L^\infty$

Lebesgue integration of $f(x)=\frac{1}{x}$ where $x\in[0,3]$

example of a sequence $f_n$, $n=1,2...$ of integrable functions converging to $f$ s.t limit of integral of $f_n$ does not exist

Prove $\lim_{n \rightarrow \infty} n \cdot \lambda(\{ f > n \}) = 0$. Where $\lambda$ is the lebesgue measure.

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