Question

When is $|x|^a|\log{|x|}|^b$ integrable over $B(0,\frac{1}{2})$

score 72 · Answer 1 · 2026-03-29 16:20:10

72

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When is $|x|^a|\log{|x|}|^b$ integrable over $B(0,\frac{1}{2})$

Published on 29 Mar 2026 - 16:20

score 94 · Answer 2 · 2023-04-25 00:10:03

94

Views

Convergence in measure of sequence $f_n(x)=|\sin(a_n x+b_n)|^{p_n}$ with $p_n\rightarrow\infty$.

Published on 25 Apr 2023 - 0:10

score 31 · Answer 3 · 2026-04-09 04:04:10

31

Views

Property Riemann Lebesgue in trigonometric integrals

Published on 09 Apr 2026 - 4:04

score 56 · Answer 4 · 2026-04-07 09:53:29

56

Views

$\Vert f \Vert_{\sup} = \Vert f \Vert_{\infty}$ in $C_0(\Bbb R)$

Published on 07 Apr 2026 - 9:53

score 34 · Answer 5 · 2026-04-11 17:19:51

34

Views

"$x^p \sin(\frac{1}{x^q})$" absolutely continuous / of bounded variation

Published on 11 Apr 2026 - 17:19

score 43 · Answer 6 · 2026-04-09 09:26:46

43

Views

$\sum_{x\in X}|f(x)|=\sup\left\{\sum_{x\in F}|f(x)|:F \subset X\text{ is finite set} \right\}$

Published on 09 Apr 2026 - 9:26

score 86 · Answer 7 · 2026-03-31 04:05:33

86

Views

(Uniform) continuous function $f : [0,\infty) \rightarrow \mathbb R$ is Lebesgue integrable, then $\lim_{x\rightarrow \infty} f(x) =0$?

Published on 31 Mar 2026 - 4:05

score 63 · Answer 8 · 2023-04-25 19:24:00

63

Views

Convergence of series $\sum_n|b_n g(nx+a_n)|$ in a set of positive measure implies convergence of $\sum_n|b_n|$

Published on 25 Apr 2023 - 19:24

score 158 · Answer 9 · 2023-04-26 01:30:19

158

Views

$|\int f |≤\int|f|$ in complex

Published on 26 Apr 2023 - 1:30

score 144 · Answer 10 · 2026-04-11 17:13:21

144

Views

Are absolutely continuous functions with values in a Hilbert space differentiable almost everywhere?

Published on 11 Apr 2026 - 17:13

score 118 · Answer 11 · 2026-03-26 12:52:13

118

Views

Compound Poisson Distribution and its Expected Value

Published on 26 Mar 2026 - 12:52

score 103 · Answer 12 · 2026-04-01 11:31:19

103

Views

What conditions ensure that $\lim_{x \to 0+} \log(x) \int_0^x f(t) \, dt = 0$?

Published on 01 Apr 2026 - 11:31

score 273 · Answer 13 · 2026-04-12 00:29:50

273

Views

Please tell me good introductory Lebesgue integral books which include a rigorous proof of the change of variables theorem.

Published on 12 Apr 2026 - 0:29

score 55 · Answer 14 · 2023-04-29 18:30:38

55

Views

Why if $\phi \in L^1(\mathbb{R}^d)$ then $\int_{|x|>R} |\phi| \ dx < \epsilon $

Published on 29 Apr 2023 - 18:30

score 100 · Answer 15 · 2023-04-30 18:51:13

100

Views

Rate of decay of $I_n=\int^\infty_0 e^{-t} \big|\sin(nt +b_n)\big|^n\,dt$

Published on 30 Apr 2023 - 18:51

List Question

When is $|x|^a|\log{|x|}|^b$ integrable over $B(0,\frac{1}{2})$

Convergence in measure of sequence $f_n(x)=|\sin(a_n x+b_n)|^{p_n}$ with $p_n\rightarrow\infty$.

Property Riemann Lebesgue in trigonometric integrals

$\Vert f \Vert_{\sup} = \Vert f \Vert_{\infty}$ in $C_0(\Bbb R)$

"$x^p \sin(\frac{1}{x^q})$" absolutely continuous / of bounded variation

$\sum_{x\in X}|f(x)|=\sup\left\{\sum_{x\in F}|f(x)|:F \subset X\text{ is finite set} \right\}$

(Uniform) continuous function $f : [0,\infty) \rightarrow \mathbb R$ is Lebesgue integrable, then $\lim_{x\rightarrow \infty} f(x) =0$?

Convergence of series $\sum_n|b_n g(nx+a_n)|$ in a set of positive measure implies convergence of $\sum_n|b_n|$

$|\int f |≤\int|f|$ in complex

Are absolutely continuous functions with values in a Hilbert space differentiable almost everywhere?

Compound Poisson Distribution and its Expected Value

What conditions ensure that $\lim_{x \to 0+} \log(x) \int_0^x f(t) \, dt = 0$?

Please tell me good introductory Lebesgue integral books which include a rigorous proof of the change of variables theorem.

Why if $\phi \in L^1(\mathbb{R}^d)$ then $\int_{|x|>R} |\phi| \ dx < \epsilon $

Rate of decay of $I_n=\int^\infty_0 e^{-t} \big|\sin(nt +b_n)\big|^n\,dt$

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